Will the cores I have in my vassals expire in 50 years, and if yes, how to I annex them before that happens?
Cores you have on provinces of your own culture group (French, in other words) will never expire. You don't have to worry about those. However, any cores on non-culture provinces will indeed vanish after 50 years. You can check by going to the province view and looking at the tool tip of the shields; it will say if the core will expire or not. France starts with cores on some Flemish provinces, including Antwerpen, and you do need to us these before 1449 or you'll lose them.
As far as your vassals go, there's no rush to annex them and their troops will come in handy meanwhile. You get missions for annexing some of them too, which give extra rewards for doing so - so best to wait for those missions to appear. Otherwise you have two options:
1. Warlike. Insult them down to below 100 relations, break your alliance, then break vassalage, then declare war. The only danger here is that in the obligatory 1-month gap between you breaking their vassalage and declaring war, they might have allied with someone powerful.
2. Peaceful. Get their relations up to over 190 and the option to annex them should appear. Your chance is improved if you have a high DIP king, a lot of countries in your Sphere of Influence, high prestige and low infamy. I think there's also a bonus for how long you've had them as vassals, which becomes significant after 30 years. You'll lose a point of stability when you annex them. Also, you can only annex one country every 10 years; but there's a slightly gamey way around that if you pause the game, then send out annex requests to up to five countries simultaneously.