As there is no public transport to speak of in the Luberon, a car is essential in order to see something of the region. You can rent a car from all the major companies at your arrival point in France - airport, station, port, etc.

Note that Avignon has two train stations. Coming by TGV train or the Eurostar direct from London you will arrive at Avignon TGV station. If you are coming on a local train you will come into Avignon central.

You can book your Provence car hire here using the authoritative Auto Europe, which gets the best deals from all the major firms:

A couple of pointers about renting a car in France...
Not all cars have air conditioning, the cheapest bands usually don't. In summer you will want a.c. in the car. It will say when you book online if a car has a.c.

And if you don't like stick shift/manual, make sure you book an automatic. Stick shift is the norm in Europe.