I think he was bored and lonely but I don't think he regretted what he had done. He had Wallis and she was his passion. He had managed to shake off the weight of duty and responsibility, and I think all he regretted was that he had nto been able to hold onto enough royal status to get back to the UK now and again and probably do the odd engagement when it suited him.
I don't think he liked living in France all that much but he knew he could not live full time in England..
I agree that he didn't regret abdicating at all but I do wonder if he regretted that his life had not turned out to be as he had hoped. It was devoid of purpose. A sense of loss over that possibly.