In the south of Belgium there's a lot of sportclimbing. That would be approx. two hours drive from Laon. You can find all the info you need here
Close to Paris, there's also the bouldering mekka of Fontainebleau. That would also be about two hours driving from where you are. Actually a nice place to spend a day or two with family.
There's also good climbing in the Vosges, a mountaineous area close to Strassbourg. But that's a bit further away.
For Mont-Blanc area: a good introduction to possible routes is Gaston Rebuffat's '100 plus belles courses', originally in French but it also exists in English (there's one on my bookshelf). Unfortunately, it's not in print anymore. There's plenty other good guidebooks though.
But, from where you are, you can basically get to most of the Western Alps quite easily. If the weather is bad in Chamonix, there's a good chance it's better in the south of Switzerland or in Italy (e.g. Aosta valley). So when planning, also look into some things in those areas, as a back up plan. Aosta valley has an easy access from Chamonix through the MB tunnel.
I also find this
site interesting for inspiration (recent trips gallery).