I think the parents will have a larger part as things go on, if not directly, then indirectly. Both know more about history and mythology than many their age, their parents have read to them, shared stories, and they understand that there is more to the world and history than is known at this time. I think that is what allows them both to be open to what is going on and while scared, not as "freaked out". they know that there are many things we do not know about how the world many centuries ago.
Whether the parents know Flamel or not I am not sure. It would not surprise me if they had met him at some point in their careers, but how much of a part such a meeting may play is unclear yet. But I would guess they will play at least some role in coming stories as the battle lines are drawn and everyone is forced to decide which side they want to be on.