You can't get more old school than this--Au Petit Bar. "Old-school, family-owned cafe & 24-seat bar offering homestyle bistro classics alongside wine."
If you look at the photo, you'll see the zinc bar with a door at the end. While we were having dinner, the door opened and a man rose out of it! It apparently led to a basement staircase. Mom and son have owned and operated Au Petit Bar since 1966. The beef dish that I had ordered was cut into rounds with beef drippings drizzled on top--just the way my mom (her mom was 100% French) had served the same dish. It brought back a memory I didn't even know I'd had. The ages of the patrons seemed to be early 20s and much older. The 20+-year-olds drifted in one-by-one and stood at the other end of the bar, ordered drinks and chatted away. I have to get back in September!
You'll have to journey out from the Trocadero, though--24-minute Metro ride.