Well coming from someone who grew up being told I had "chicken scratch" or that I would become a doctor because my penmanship was so horrible, I never fully corrected it, and I'm now 30! I am surprised that his penmanship is causing his GPA to fall. Usually, the writing class and teacher judge students on theirs thoughts and how they get them on paper, not how it looks. However, I have heard teachers, and I did to an extent, say that if they could not read or understand the handwriting they would give the student an F. For your son I would suggest talking to the teacher first. S/he will let you know exactly needs to be done. I would suggest he use the computer to type his papers or other homework. It is difficult these days because so much is done on the computer with little practice working on one's penmanship. Having and open and honest dialog with your son and letting him know his handwriting needs to improve because when he gets a job or to college, it might work against him. In my case I knew my handwriting was awful, and I didn't want to change it. It was difficult to do but I had to force myself work at it. I am still working at today, but at least I am aware of it and know I needed to improve it.
 

donpotter.net has a lot of stuff about reading, writing, cursive, etc. He sent me a bit about the Palmer Method. It's how everybody learned to write before the schools went downhill. I was thinking how odd it might seem for kids today--that kind of precision. But if you presented it as a graphic design project--maybe it would appeal. I mean, that's where you take the time to make pretty letters for their own sake. Like a chef making cookies....
Here's link on YouTube: See below. I would encourage your son to treat it as an interesting challenge: can he do what is in that video??