Spring can be early in the Alps, as there will be a lot of snow still, short days and cold temperatures. But it is possible of course ;o)
And if you go to lower altitude you shouldn't encounter as many obstacles.
Everybody is usually extatic about the Mont-Blanc range. Personnally I'm a big fan of Les Ecrins
Fewer people and wilder area. But in Spring it might be more difficult to access it as certain roads may be closed, and some huts too.
It really depends on what you want to do... any idea ?