Corsica is awesome! I'm very lucky though bcause the inlaws have a place in a wee village called Lumio in the north, not to far from Ile Rousse and Calvi.
Check out Fango valley the river pools are awesome and the road up that way from the airport would make for a cracking road ride. Be warned though the locals drive like lunnatics, and the roads are alot busier in the summer. The dude above is right about the heat, if your going to ride you want spring or autumn otherwise you will cook.
There is a book of mountain bike routes on the island, can't remember who its by but google should find it, the whole island is covered in trails all marked with paint flashes the climbing is great too, there are hundreds of bolted sport routes, and because of the GR20 the mountains are full of huts to overnight.
I like the north more that the south, more mountains and less tourists, the south has flatter land and more big resorts.