use "chez" with your last name or an elegant last name. Chez is like 'our house' or our restaurant', a lot of french restaurants have Chez in their name. Maybe 'Chez Waldorf' or 'Chez Antionette' lol. Lumière is a popular french restaurant in Vancouver
"Isabelle" is a name, so you spell it "Isabelle" in French or any other language. "Restaurant" is originally a French word, so it's spelled "Restaurant". The possessive in French does work a little differently... I'm not positive, but I think the whole thing would come out as "Restaurant Isabelle".
Sax is a really great hotel, in the downtown Chicago area. With many excellent reviews on the hotel from people who have stayed there. But there are also many restaurants near this hotel. Not with the name Sax though.