So, I looked it up and both are fine. Without the 'n' is just the original French term, which language we got restaurant from as well, whereas with the 'n' is reasonably common, more-so in the US than the UK, (which is geographically and culturally close to France).

Going by our grammar it amounts to restaurant and eur, which functions the same as er in many English-based words, but gets used for words that we got from French. The suffix er just means 'do-er' or 'one who does'. So it makes sense that folks would lean towards the more English-ified version of the word. We kept the eur because it's a French word, but it's no different than someone who dances being a dancer or someone who owns being an owner.