I have a similar situation (I'm plat, my wife and kids all silver) and was chatting with an agent at CDG once when we were all travelling together. She told that the policies were:
-The whole family can use the SkyPriority lines for check-in, security and immigration at CDG, for the outstations it depends on each airport's policies (for example, at YVR they put fast track stickers on all our BPs at the checkin desk so we can go through priority security together)
-You can bring your kids in the AF lounges for free during school vacations. During other periods there is discounted paid access for them (I paid 20USD for each of the kids at JFK once).
-Only bags checked under my name get priority as it's coded by the computer and the agents don't have any leeway, but in practice they usually all come out together.

This is what i was told, and I've never seen these in writing anywhere, so it may not be totally accurate, but my experience over the last couple years has proven it to be accurate.