Well getting any info out of the French Embassy is a big pain.. here is what I would do...

Take 2 (or maybe even 3 or 4) appointments for the same day for yourself and your family. One of your appointments will be first, and at the time they call you, mention that you are a family try submitting all the documents. That way if they refuse at least you still have a chance for the same day.

In the past I have seen families going to the counter at the same time. But better to have a hedge in having multiple appointments the same day.