I worked for a company for 15 years as a sales manager.

I gave notice and accepted a job in another state.

My old employer is now telling the customers that he had to let me go.

What can I do about it.

You can sue of course, anyone can sue anyone, but it's going to be tough, especially long distance. You need paperwork showing you quit. You need affadavits from people who were told that you were fired. You need to show that you were harmed and how. You need to file in civil court, and usually paying a lawyer to do it is going to keep you from having to spend a lot of time on it.
Your best bet would be to contact as many of those people as you can and prove to them that you quit. It probably is important in the long run, since people even far away often run in the same business circles.

You have a job in another state. So I assume , you no longer have anything to do with HIS customers. So just forget it and move on.