Is there a sin in a man loving another woman while his wife is still with him? And what should he do in this situation?

Unintended feelings of love, which did not lead to committing what is forbidden, are not blameworthy. You did well by avoiding them. If you wish to marry her and believe you can be just, then do so, for the Prophet, peace and blessings be upon him, said: "There is nothing like marriage for those who love each other." If it is not possible, then turn your heart away from her and seek Allah's help, for whoever is truthful with Allah, Allah will be truthful with him. It is not permissible for a woman to refuse marriage because she is attached to you, as this entails missing out on good and creating tribulation.