Breach of Contract Claim for Copyright Infringement
This was the situation in the case of Effects Associates ["EA"] vs. Cohen from the 9th Circuit Court of Appeals. Cohen verbally hired EA to prepare some film footage. Because he was not completely satisfied with the footage, Cohen paid EA only half of the agreed amount, but used the footage anyway. EA sued Cohen for copyright infringement. The court held that EA had granted Cohen an "implied" license for the work based on its conduct. Although it dismissed the infringement case, the court noted that EA could sue Cohen in state court on a breach of contract claim for not paying for the license.
We can learn a few things from this case. First, put your licenses in writing. You don't want a court deciding what you meant to do. As the court in the EA case explained, "[putting agreements in writing] prevents misunderstandings by spelling out the terms of a deal in black and white, forces parties to clarify their thinking and consider problems that could potentially arise, and encourages them to take their promises seriously because it's harder to backtrack on a written contract than on an oral one."
Second, make your licenses subject to being paid in full. This language can include: "Until we have agreed to the terms under which you will use [the work] and have paid me the agreed-upon fee, you have no rights to make any use of this work. Any unauthorized use constitutes a willful infringement." A court will not input such requirements into a contract absent "plain, unambiguous language." Without that condition, like EA, you may forego your right to pursue an infringement claim.
Finally, as a copyright holder, you are the "master of your claim" and can opt to pursue copyright infringement or breach of contract when someone uses your work without permission. The facts of your case may dictate which option is best for recovery. An attorney can help you make that decision. But whatever you do, decide to protect your work.
Take my advice; get professional help.