It seems reasonable to think that language should be relatively logical. The problem, especially with English, is that it totally isn’t. You have one mouse and many mice, so why don’t you have one house and many hice? You have one goose and many geese, but you don’t have one moose and many meese. And how is that flammable and inflammable mean the same thing? English is weird.
You can attribute a big part of this to the fact that English is effectively a mish-mash of several different languages. In particular, many English terms borrow from the French and maintain at least some of their French origins as a result. And herein lies the confusion between restauranteur and restaurateur.
But it’s not just about pronunciation; it’s about spelling too. Restaurateur is a French word for someone who owns or runs a restaurant. My parents were restaurateurs for a great number of years and it is perhaps through working in these restaurants that I developed my sense of work ethic. The lack of an “n” in the word can be awfully confusing to English speakers (and readers), because what on Earth is a restaurat?
And so, it’s not at all uncommon to see people spell the word as restauranteur (with an “n”) instead. This follows a similar kind of construction as we find with words like entrepreneur, chauffer, connoisseur, and amateur. Except, technically speaking, it’s wrong.
A quick Google search for “restaurateur” yields nearly 13 million results, whereas a search for “restauranteur” comes back with about 800,000 results. That’s a ratio of over 16-to-1. Unsurprisingly, popularity of the latter spelling stems mostly from the United States, going as far back as the mid-1800s.
Realistically, not too many people are going to call you out for spelling the word as restauranteur. That said, if you want to add a certain je ne sais quoi to your writing by introducing some borrowed French terms, you’ll want to avoid this faux pas of adding the extra “n” and spell it as the original restaurateur instead.