A man was given a sum of money by a non-Muslim, and he performed Hajj and Umrah with it. What is the ruling on his Hajj/Umrah?

All schools of thought allow accepting a gift from a non-Muslim as long as it does not glorify or endorse their Shirk.
Using this money to go to Hajj or Umrah is permissible as long as the person does not compromise any Islamic values in accepting such a gift.

Below, please find a usual classical quote you would see in classical Fiqh books:

“A non-Muslim’s gift related to acts of obedience and devotion is permissible. However, this gift must not include bribery, lead to affection for or allegiance to the non-Muslim, or result in compromising any rulings of Islamic law.”