Informal:
* Jean et Marie sont finis. (This is the most literal translation)
* Jean et Marie ont rompu. (This means "John and Mary broke up.")
* Jean et Marie ne sont plus ensemble. (This means "John and Mary are not together anymore.")
Formal:
* Jean et Marie ont mis fin à leur relation. (This means "John and Mary ended their relationship.")
More specific:
* You could also use the verb "se séparer" which means "to separate" if you want to imply that they are no longer living together. For example: Jean et Marie se sont séparés.
* If they have divorced, you would say "Jean et Marie ont divorcé."
It is also important to consider the level of formality and the context of the situation when choosing the appropriate phrase.