Hi, Mike —
The first question to ask the man is what is the religion of his first spouse.
If she was a Catholic and the ceremony was only a civil ceremony then the Catholic Church does not recognize that Marriage and the man and his new wife would not have to do an annulment but rather what is called a Lack of Form case (i.e. his former wife was obliged as a Catholic to be married with a dispensation from the Church and she didn't, so the marriage lacked form and is manifestly invalid).
Now if she was not a Catholic (or she did get the proper dispensation) what you had was a perfectly valid marriage.
The Catholic Church doesn't just recognize Marriage as an exclusively Catholic thing but as a universal right and action.
- If two Jews get married we recognize it just as we recognize that Mary and Joseph were married.
- If two Muslims get married we recognize that as a holy action from God, and
- even if two people of no faith get married we recognize that as a perfectly valid action and from God (just not Sacramental unless they were both baptized).
The bottom line: We recognize all Marriage as holy and from God as they are Natural Marriages so although the Catholic Church had nothing to do with it, the man would still need an annulment of his first Marriage in order to be free to marry his Catholic girlfriend.
Go to her local priest to begin the process.