With Jack & Mary (gorgeous!), I would go for something storybook sweet and classic like them, and visually cohesive.
Everett “Rhett” would be my choice of your contenders.
I like Augustine as a middle, it complements Peregrine but too lengthy and complex imo, compared to the others. Maybe August, Arthur or Angus instead?
Wouldn’t choose Clark, too similar to Jack to me and I really like Francis but I don’t love Frank - it’s a bit honky and harsh to me, and maybe also a bit close to Jack (but without the cool breeziness of Jack). Could Francis be a middle? It’s very handsome, Frank just isn’t as appealing to me.
I think Alice and Clara would be lovely - I prefer Clara myself and it would be my pick of the two - but it is a repeat of Claire (if you ever use it) - though you might anyway like that connection.
I like Jane but I would probably go for different starting letters - so have it as a back up (so it’s not Jack and Jane). I also think having different endings is nice too (hence why Clark & Frank wouldn’t be a top pick).
Other ideas:
Anne/Annie
Iris
Tess (possibly as a nn for Therese)
Grace
Eliza
Violet
Rose
Agnes
Cecilia
Louisa
Imogen
Thomas
Walter
Wesley
Vincent
Lucas
Callum
Edmund
Tobias
Hugh
Hugo
Leo