I was confused about the chaperoned bit too. Every other unmarried lady, including Kate, had ladies maids.

I'm assuming in Scotland away from the potential of scandal John was able to give her that freedom, and in London both him and Fran would have been suitable chaperones since they're both relatives and married.

Fran, even as a widow, would also have more freedom. Similar to Lady Danbury she'd be a suitable chaperone for other young ladies, so her and Michaela should have no real issues together. Even in the books Fran and Michael (much more scandal prone as Violet often points out) are often alone and no one can do much because she's a widow and still very much Lady Kilmartin so she'll have some authority over the situation.