I'm not sure it even matters.
If it gets to court you've got a plaintiff either claiming that defendant violated copyright or the defendant failed to follow the terms of GPL.
In both cases the defendant will respond that they followed the terms of GPL.
In both cases the court has to determine what the license means and then whether or not defendant followed the terms of the GPL. To do that the court has to decide what those terms actually mean.
For that I don't think it matters if GPL is considered to be a "contract" or "license" because as far as I have been able to tell the rules of interpretation are the same no matter how you characterize the document.
Maybe it could make a difference in the remedies that are available if plaintiff wins. If it is seen as not being a contract then it might be that the only remedies would be those under copyright law. Those would generally be an injunction ordering defendant to stop infringing and monetary damages. Actual monetary damages would be near zero so plaintiff would probably ask for statutory damages.
If it is seen as being a contract then potentially the remedy could include an order that the defendant release their source code. If the GPL infringement was distributing binaries without making source available this would probably be the remedy plaintiff wants.
Ordering the defendant to obey the terms of the contract is called "specific performance" and I believe is usually disfavored by courts if monetary damages are sufficient but since infringing GPL generally doesn't cause any monetary losses to the copyright owner and the whole point of the contract was to make source available I'd expect a decent chance plaintiff could get specific performance.
Note that this means that it is actually better for GPL to be seen as a contract.