Status is a personal thing; it does not apply to all passengers on your reservation. (Delta does this differently; if you had status with Delta, any passengers travelling with you on the same reservation would get (at least some of) the same privileges that you would but only when travelling on Delta flights).

The one exception: if you buy Flying Blue award tickets for your family (or, indeed, for anyone else), your Gold status will exceptionally apply to those award tickets, even if you are not travelling, but only on flights with Air France and/or KLM. So, when they check in, their boarding passes should state "Sky Priority", and the boarding passes should also allow them to access Air France and KLM operated lounges. This is an unpublished benefit, and it may not always work 100%, and when it does, it only works when you are flying on Air France and KLM flights and probably only when using lounges that are actually run and operated by Air France or KLM; none of the other Skyteam or Flying Blue partner airlines participate in this "fiction", so you can only reasonably expect your status to "carry over" to these passengers in so far as whatever benefit is in question would be the responsibility of Air France and/or KLM to provide.