The problem is that after their original patent expired, they sat on their hands for too long. By the time they tried to trademark in 2008/2009, their bodies were considered generic in the US. Gibson, on the other hand, did what Fender should have done and applied for trademark (for their Les Paul body) back in the late 80s.

Now other brands are eating their lunch, and Fender is seemingly trying a last hail marry to get this settled. My guess is that if they manage to get a positive ruling in Europe, they'll somehow try to use that as case for US courts.