I'm pretty sure ASMPA-R is precise enough to be considered tactical, and the fallout small enough to easily consider its firing over blue water. Yes, the number of French tactical (sorry, "pre-strategic") nuke is limited (around 50), but i think that's enough of a detterent.
It's not about the precision, it's the yield. We've divested our tactical options back in the 1990s because our nuclear policy is one of strict sufficiency and all our nukes are above a hundred kilotons of TNT. That doesn't leave a lot of room to thread any needle.
Also, our nuclear doctrine says that it's a nuclear warning shot, meaning that the next step on the ladder is French-delivered Armageddon by SSBNs. We're not supposed to keep lobbing them in case of a persistent problem.