Recently, in the final game of World Cup, French midfielder Zinedine Zidane headbutted Italian defender Marco Materazzi for insulting him.
In the aftermath, Zidane apologized in an interview with a French television but added that he didn't regret hic actions.
Can one coherently apologize for an action yet not regret that action? Or is Zidane false in one of his claims (the apology or the lack of regret)?
That depends on exactly what he was apologizing for, and what he meant when he said he didn't regret the action. I'm sure that he was genuinely sorry that his action caused embarrassment and shame to France. That is quite consistent with believing that he was justified in his action, and that he would do it again in similar circumstances. That is probably what he meant by saying that he didn't regret the action. Of course, he might just have been inconsistent. There was an enormous amount of pressure on him to apologize. I suspect that most public apologies are insincere.