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Being blunt here: If you'd come to me and say "Hey, I have a great idea that can save us tons of money, but I need to see some cash before I will talk about it", I'd fire you on the spot. This feels like blackmail to me and I won't have it regardless of how much money is at stake.

However if you show with a detailed record of your achievements: "Hey boss, look at all the cool stuff I've done and the money I saved for the company. I think I provide way more value that my current compensation represents", I'd be more than happy to have constructive discussion around that.

All of that depends of course on local laws and personalities involved, but threatening to withhold the idea in order to force something can backfire badly.

Look into your employers handbook and into national law. There are laws regarding inventions and how they should be remunerated (at least in Germany, but I guess this is true for many countries). Important: There are countries where you are legally obliged to inform your employer about an invention!!

This is the French law, as you wrote in a comment about being french.

In Germany, you would file an invention report form and submit it to your employers ip (intellectual property) department. They decide if the idea is worth claiming for themselves or not. If not you own the idea and are free to file for a patent. If they claim it, they decide if they want to keep your idea a secret, publish it publicly or file for a patent. If they chose one of the first two options they have to get your agreement. Either way they will remunerate you a certain amount of money. If a patent is claimed, there are legally based algorithms to determin your remuneration.

So much about getting paid for your invention. If you are employed as a developer, your employer might expect you to make inventions. This means, your inventive thinking is already paid for in your normal salary. In the case that you can't be expected to regularly invent things, you might be able to negotiate a higher salary. I definetly would mention the invention in the next review.

Get in touch with a lawyer !

Don't aim for a raise but a one off payment, multiple payments or licensing agreement.

Make sure the contract (oh yes) is completely independent from your work contract and your work / employer.

If you'd negotiate for a raise, what would stop the company from letting you go after a few months?

Since you say, by law your idea belongs to the company, your negotiating position is weak at best, non existant at worst.

So talk to lawyers specialized in employment and patent / intellectual property laws.

See if you can patent it yourself after all to have the strongest negotiating position.

...Oh btw. it can make a lot of sense to have a very expensive, professional or luxury product.

Production is less ressource intensive than mass production and the profit margins are considerably higher.

Selling more brings also additional distribution and advertisement costs as well as dangers of oversaturating the market.

Reducing the price could raise the risk of devaluating the product or its image.

As you said in the comments, your idea belongs to the company. It's still only in your head now, and we don't have thought police, but as soon as that idea is put on paper or told to anyone it's your company's property. You don't own this idea and you can't use it for negotiating a deal. The only 100% legal options are sharing the idea or forgetting about it.

If you tell them you have a good idea but you want a raise first, you're gonna get fired after you share the idea, it's highly inappropriate and borderline breach of contract to play your cards like that. They'd be crazy to keep you, what if you're gonna ask more raises in the future for simply doing your job? You're essentially taking the idea hostage, only releasing it on your terms.

The only possible way of getting something out of this without risking your job I can think of is negotiate a percent-of-revenue deal now, wait, then bring up the idea later to boost the company's revenue. Another way of dealing with this situation could be to negotiate a raise, ask for requirements for a raise if they decline, and share the idea without any demands. If your idea meets the requirements for a raise then you have your raise, but even this is unethical at best.

The only way to handle this like a professional is just sharing the idea without any strings attached, then schedule a meeting to ask for a raise, provide this idea as an argument as to why you deserve a higher pay and update your resume if they decline.

Whatever you may decide to do: get a lawyer. Don't go doing anything here without legal advice, don't take the internet's suggestions at face value, a whole lot more than your job can be on the line here.

First, let go of the idea that you deserve a slice of the money this represents. Legally it's not true, and practically it won't help you. The better attitude to take is that you're the sort of person who can (and does) come up with things like this. That makes you a stellar employee, and you deserve to be respected, appreciated, and paid as such. You like the people you work for and the environment you work in, and that's great. Taking this attitude will help you keep that.

My suggestion, then, would be to schedule a discussion with your boss. Figure out how much engineers at your level of experience are usually paid beforehand, and figure out how much you, as a stellar example of an engineer at your level of experience, want to be paid. Personally, I tend to nudge it down a bit after I've done that in the interests of workplace harmony, but you do you. "How do I figure out how much I'm worth" is a whole other question, and I won't get into the details of it right now.

In that discussion, lay out the basics thus far. You came in not really knowing how much you were worth, and with them not really knowing how much you were worth. You think you did poorly on the initial negotiation and wound up pretty low for your field. Since then you've done X, Y, and Z useful things, saving the company roughly Q amounts of money. Then you pull out the showstopper. "I've also come up with a new process improvement that I think will really blow you away." At that point you lay it out fully. You explain it so that they can understand it. If they call people into the office, you teach it to them. Whatever it takes. When you're done, you come back to the salary thing. "So, boss, given all that, how much am I worth?" - then use that as a starting point for negotiations, if it's not high enough to begin with.

If you present it in that way, there's no basis for hard feelings. Nothing gets ugly, no one has to go for a lawyer. At the same time, you're making a really compelling case that yes, they should pay you more money. At that point, if they're at all reasonable, they'll decide to pay you more money (...especially since they'll suddenly have a massive improvement in projected cashflow to pay you more money with).

The point is that right now, you have basically no leverage. You have absolutely no leverage that you can use without poisoning the well badly. As such, you can use this technique to basically gain social credit for freely giving away the leverage you don't have and creating an implied obligation to reciprocate. If they don't respond well to that, then they're indicating that they don't particularly intend to pay you well regardless. At that point you find some place that will pay you. You've certainly racked up a decent set of accomplishments.

Side note: Country of origin does matter here. I'm basing this on US companies. It's my understanding that France cares more in general about aggressively asserting and defending personal status. It's possible that going a bit more hardball would work better there than here. At the same time, you can't go too hardball because, again, you have no real leverage that you can actually use without likely destroying your relationship with these people and your career.

You are ignoring one critical fact: Your idea, on its own, is completely worthless.

It only has value if you can turn it into a marketable product. You could do that by setting up your own company and competing with your current employers (though you would need to check if your current employment contract imposes any restrictions on doing that), or more practically, you can get your current employers to make use of it.

Many high tech companies have a method of rewarding employees for ideas which the company can patent, and the "one-off" payments can be substantial (i.e. more than a year's salary). But the long term benefit to you as an employee is in demonstrating what you can do to benefit the company, aside from "what you are being paid to do".

If you want to "go it alone" to make money from your idea, then good luck - but the odds are that you will fail.

You also need to seriously consider the possibility that your idea won't actually work, for some reason that you haven't discovered yet. The more senior engineers and designers might already know that because they have already tried it, before you even joined the company!

So, your best strategy is to sell your idea to the company management, and let the rewards from it (if there are any!) come in the future.

Generally speaking, unluckily for you, you are not the owner of any innovative idea regarding your work as employee in a company.

Find here an useful reference on patents from employees in France

As a matter of facts, very few positions in French industry are of the type you could prefer in this case... in all other cases the employer is, or is entitled to become, the only owner of your inventions related to his business.

In theory, the maximum you can do, if you are so sure of your idea, is to leave your work, make your research and, after some time, come back to your company and to competitors to negotiate the experimental application.

But it can be considered at the limit of ethics boundaries, very probably out of them for many courts.

But please remember this before doing anything:

the most of the “revolutionary ideas” synthesized by a newbie in a business... result to be not applicable for some details not known or not understood.

This is cruel statistics, because any newbie knows some aspects of the problem only and underestimates industrial application difficulties.

Anyway, ask the same question in general to your boss and try to understand more about your specific contractual duty.