Channel Islands didn't really provided a clear advantage for either an insular or continental power in Europe. That various french rulers barely overlooked the possibility to take them, while you had a whole and long tendency to take over each possible harbour or inner strong places along the Channel seems to be quite telling : as far as I know, some of these islands (not considered as a whole entierly until recently) were indeed took over by French or French mercenaries but merely as an exchange trade.
Don't get me wrong : I could see a french conquest of some of these islands (again, maybe not the whole) less trough plan or interest, but sheer accidental opportunism. A TL where Yorkists are unable to take back Jersey; or a LT where Stuarts manage to somehow keep these under their authority but de facto under French protectorate.
But I don't really see why it would be an active goal, or how significant it could change even local history.