Can I just ignore broody hens and let them figure it out?
Broody hens to tend to quit eventually, if you just leave them alone and they do not have any fertile eggs.
But "eventually" can be a long time. I once had a hen stay broody for 6 or 7 weeks (it was long enough ago I don't remember the exact count, but it would have been long enough to hatch an ostrich egg.) She did not seem to have any problems from being broody that long.
I've read of a few hens that stayed broody and eventually died. Most hens will not do that, but of course there is no guarantee about your particular hen.
For broody hens that do die, cause of death would typically be starvation (if she doesn't eat enough) or parasites (if she has something like lice or mites, they can get badly out of control while she sits in the nest all the time, and eventually they suck enough blood to actually kill the chicken.) Or in hot weather, if the nest is in a coop that gets very hot, a broody could die from the heat. All of those are things you can watch for, rather than just being surprised one day.
I have read that I can put her in broody jail - I have a large dog crate. But I'm also trying to integrate two 5 week old mille fleur into the flock and it seems just too much.
The sooner she quits being broody, the sooner she will get back to laying eggs. But if you want to just leave her broody for now, you do have the option to break her broodiness later, after you are done integrating those chicks. Sometimes it is easier to do everything at once (integrate chicks with most of the flock while the broody is locked up in "jail") other times it is easier to do one thing at a time (if you have one crate and you want to use it for chicks first and broody-breaking later.)
I think it should be fine to leave her for now, and you can decide to break her at a later point if it seems like a good idea then.