The French word for a person who owns or runs a restaurant is restaurateur, with no n, and this is the spelling used most often in English, especially in edited writing. Restauranteur, with an n, appears in English about once for every ten instances of restaurateur. But while this spelling is common and has a long history, many people consider it wrong.
The Oxford English Dictionary notes restauranteur as originally from the U.S. and lists examples from as far back as 1859, though a historical Google Books search covering the 19th century uncovers no more than a handful of instances of restauranteur. Many more examples are found in texts from the first half of the 20th century, including many from outside the U.S. Today, the misspelling appears about equally often throughout the English-speaking world.
Restauranteur occasionally finds its way into edited publications—for example:
We chatted with the 39-year-old chef and restauranteur about oyster-gate, his anxiety issues and his bromance with Fabio. [Entertainment Weekly]
The would-be restauranteur, Whisk Group, has finally given up the fight. [Washington City Paper]
And here, the word is spelled in the more conventional way:
A Brooklyn restaurateur, adopted as a baby, was shocked to learn his biological father is none other than “Motor City Madman” Ted Nugent. [New York Daily News]
Umberto was shot dead on the day he learned the restaurateur had died in a shooting. [Guardian]