I've always been checked for id, even for local flights as well (SXB, LYS, ETZ, LIS, BCN, MLH/BZL/EAP). Airlines were Air France and EasyJet.
MLH/BZL/EAP is fun because you kinda keep going back and forth across borders a few times as you walk around, and depending on where you "come from" the destination country can have slightly different requirements for entering upon arrival (which is checked at the gate on departure, I did get a random customs check on arrival once when crossing the swiss/french border). Not a problem on the happy path but could get hairy if you get into trouble I guess.
I think in France it may depend on "plan Vigipirate" levels as well.
