I'm going to say it probably depends on the time of year.

I have a place about 45 minutes out of Nice and always allow plenty of time to get to the airport as the motorway can be a complete nightmare at times. I go there several times a year but the only time I have hold luggage is mid-September and I've never had any problems dropping my bag off say 2.5h before departure.
Also, I'm French in case that makes a difference to their willingness to accept luggage a bit early I've been in the UK for over 25 years so I've done a fair few flights from NCE back to London and I've not once been told that I'm too early for bag drop.

In August, or at Xmas, Easter holidays and any other time when the place is heaving, the 2 hours limit might well be strictly enforced.