Caen is not exactly "very small" unless you are comparing it to international airports.
By GA standards it is large, with two hard runways (one 1900m) and a few regional scheduled services. There was a daily service to the UK, but it may not still be running. In my experience most French airports have a "windswept" feel to them, with lots of facilities but no-one actually using them.
Airspace should not be a problem. There are low level miltary corridoors to the South, but not close to the coast. I don't have an up-to-date chart to hand, but there may be a few ZRTs to steer clear of. Caen and Deauville have had their airspace upgraded to Class D, but you should not have a problem.
I cannot help with the club or rental information. I suspect it will be difficult and expensive to arrange which ever side of the channel you choose.