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.