Who first came up with the idea of "A la carte" menu?

Didn't realise it was an 'idea'.It's French for 'from the menu' and I thought that as such it was just a term that came to be used in restaurants Worldwide.
Viv

Same thought here Viv. It's a term usually associated with a better class of dining, too.
So, with that reasoning in mind, I'm guessing it could be English in origin, and those pesky French just borrowed it from us.

"A la carte" means that you have to pay for each item separately. For instance if you order a steak at $20 , the potatoe is not included and you have to order it and pay an extra $3.00 . Anyway, someone (French) came up with that fantastic idea. Who was he?

That great chef (and even better businessman) Auguste Escoffier

Right on Fred. The encounter of Ritz, Carlton and Escoffier lead to the magnificent Hotels where Queens and high society people would stay for a short while. Escoffier

Having spent many years in the hospitality business, I feel it necessary to point out that what seems like a consumer rip-off (paying for every item on your plate) isn't quite as it seems. Consider what the price would be if all the side dishes would be included in that price. I assure that, in your example, the steak with the necessary potato would be higher than $20.

At the Seminole Hard Rock Casino (Where Anna Nicole Smith passed away)there's a restaurant where he filet mignon sells for $45. à la carte. That of course do not includes the tax & gratuity.

A good reason for 'a la carte' is that it deters people from ordering 'a la carte' In France the practice is to take the menu/ one of the menus of the day.The price(s) are fixed. The choice is limited to what the kitchen has got in and is prepared to cook, or, in some places, what the chef wishes to cook and be judged on .This applies at all levels fom the humblest bar to the Michelin starred topmost restaurants. Only the eccentric, the perverse and the fussy opt for 'a la carte' unless they are asking for something very simple the preparation of which won't disturb the kitchen e.g an omelette or a steak. (Just to give a hint , the restaurant normally has the same dishes as are on the 'menus' listed in the full 'carte' as each main dish plus the accompaniments listed individually. Then the customer can see how much cheaper it is to have the menu)