Does she have to leave her husband if he does not become Muslim?

Praise be to Allah.

If a woman becomes Muslim and her husband is a kaafir, then the marriage is annulled, but she may wait until the ‘iddah ends, then if the husband becomes Muslim during that time, then she is still his wife, but if he does not become Muslim before the ‘iddah ends, then the annulment of the marriage becomes clear, starting from the time she became Muslim. 

Can he go back to her if he becomes Muslim after the ‘iddah ends? 

There are two scholarly opinions concerning that. The more correct view is that he may go back to her if she agrees, because the Prophet (peace and blessings of Allaah be upon him) sent his daughter back to Abu’l-‘Aas ibn al-Rabee’ several years after she became Muslim, when he also became Muslim. 

But if she refuses then they must be separated by force by the judge. End quote. 

Shaykh Ibn ‘Uthaymeen (may Allaah have mercy on him)