I don't see
Jack being too trendy at all; in fact, I don't really hear it much nowadays. I also don't think it's too informal, although I can see why people would see it that way.
To be honest though,
Jack seems not to fit with
Edmund Francis too well. The only reason being that
Jack seems a bit more of an upbeat name to me... so in a way, I do prefer
John Edmund Francis (nn
Jack)