Since a restaurant owner is called a “restaurateur,” it seems like the n in restaurant got discarded along the path to creating the word restaurateur. Either that, or we later decided to toss an n into the word restaurant just for fun.
Stranger things have happened in the English language, but the real story is a little more logical. As etymologist Michael Quinion explains on his blog World Wide Words, both words come from restaurer, French for “to restore.” Restaurant is the present participle form of the verb (restoring, in English), and restaurateur describes a person who restores something. Because English speakers are so familiar with the word restaurant, some people assume that the -eur is a suffix tacked onto restaurant. In reality, restaur- is the root, and -ant and -ateur are two different suffixes. An English example might help clarify the point: You wouldn’t wonder why a person who bakes is called a “baker” instead of a “bakinger.” It wouldn’t make grammatical sense to stuff the n from -ant into -ateur, even though they both already have an a and a t in common.
Furthermore, restaurateur didn’t always mean “a person who owns or manages a restaurant.” A French restaurateur was once a literal restorer—a handy worker who fixed broken objects. Later, in the 1600s, restaurateur described a surgeon’s assistant responsible for setting broken bones. The word restaurant, meanwhile, was used for a meat-based broth meant to restore health (though it was also sometimes used to refer to curative food and drink in general). By the late 18th century, it was common for people to open eateries to serve their meaty broth and other restorative fare. The owners became known as restaurateurs, and the places themselves were eventually called restaurants. As skilled cooks formerly employed by aristocrats started working in (or founding their own) restaurants during and after the French Revolution, the restaurants expanded their offerings beyond the basics.
It didn’t take very long for misguided English speakers to start sneaking an n into the word restaurateur once it entered the English lexicon. According to the Oxford English Dictionary, the first known mention of a restauranteur comes from an 1837 letter written by former British prime minister Benjamin Disraeli. It’s been popping up ever since, much to the chagrin of pedants and people with a basic understanding of French morphology.
[h/t World Wide Words]