We've used AutoEurope for our two rentals and both times the best deal was with Europcar. We had automatics both times (it's been way too many years since hubby drove a standard and I couldn't if my life depended on it). No issues getting an automatic - but we did pick up at larger garages - Paris the first time and the TGV stn in Avignon the second.
If you end up with Europcar, we dropped ours in Nice the second time. I thought I was saving money by deciding to drop it at the location in the downtown (rue gustav V) instead of at the airport, as there is generally a surcharge for picking up/dropping off at airports and large train stns...in this case, it was about $40 to drop at the airport. I should have bitten the bullet and dropped it at the airport - the hassle we had trying to return it to the downtown office - we missed the little road, had to get turned around, finally made it back, only to be told we had to go one street back and drop it at the garage - and of course it was a one way street the wrong way so back out and around again and the traffic was horrendous - I swear it took 45 min from when we initially missed the street to getting the car in the parking garage.
I guess it would depend on where you are leaving from when you are finished in Nice - will you be flying out from the airport or taking the train?