http://www.doornmore.com/

You can get any door style, wood species, glass insert you like in both french and single doors.

In my experience with kids, they want to be with you every second. So I would leave the door between kitchen and playroom open. For a while there will be constant "remember, toys stay in the playroom" reminders but at least to me that is preferable to the constant sound of doors opening and shutting and someone calling from behind closed doors for me to "look at this". Whenever you can be in voice contact with kids, it's best imo.

They do sell single doors that have glass that matchs the French doors.

I agree--match the french doors with a single. It's true that you might end up having the doors open while the kids are in there, but the doors will be a nice upgrade anyway, whether it becomes a dining room again or not.

You could also do a solid door to the kitchen in the same style as the French doors--just with wood panels instead of glass (or painted). That's fairly traditional and would look nice. Older homes wouldn't let you see into the messy kitchen while dining so they'd skip the glass on the door to the kitchen. Trim out both doorways the same, regardless of door style.