Does Franklin have a playdate for the 2yo class? DS went there for the 2yo program, and I don't recall a playdate, but thought I heard there was one for the primary program. I thought it was first-come, first-served for 2yo.
Don't stress about it, OP. Parents stay in the room. Most parents sort of sit back and don't interact w/ their kid too much (try to let the kids play on their own), but I think that's just so it doesn't look like your kid is incapable of any self-direction and/or to avoid looking like a helicopter parent. The teachers will try to go around to each kid for a minute or two to interact with each kid. If your kid does want to engage you, that's totally fine.
There's often a snack portion of the playdate. One helpful thing to teach your kid is to clean up when he or she is done. They also use little paper cups (the bathroom size), so if your child has never drank from an open cup, you might want to do that.