Is a divorced Jew, whose former wife remains alive, obligated to obtain an annulment of his marriage in order to marry a Catholic widow in the Church?
An annulment is a declaration that no marriage was validly contracted from the beginning. But a marriage between two unbaptized non-Christians is presumed valid by the Church unless proven otherwise. So, yes, a Jewish person who had been married to another unbaptized person would need to have his marital situation regularized before he would be free to marry a Catholic.
If the Jewish person had converted to Christianity and was baptized while his former wife remained unbaptized and chose to end the marriage, it is possible that he might qualify for the Pauline Privilege, which is based on this passage of the apostle Paul:
To the rest I say, not the Lord, that if any brother has a wife who is an unbeliever, and she consents to live with him, he should not divorce her. If any woman has a husband who is an unbeliever, and he consents to live with her, she should not divorce him. For the unbelieving husband is consecrated through his wife, and the unbelieving wife is consecrated through her husband. Otherwise, your children would be unclean, but as it is they are holy. But if the unbelieving partner desires to separate, let it be so; in such a case the brother or sister is not bound. For God has called us to peace. Wife, how do you know whether you will save your husband? Husband, how do you know whether you will save your wife? (1 Cor. 7:12-16)
The Pauline Privilege is different from an annulment because it ends a valid natural marriage. Only a sacramental marriage cannot be dissolved, except by death. Both parties must be baptized in order to contract a sacramental marriage.