That actual relationship was apparently the result of Berry and Jackman building up some background for their characters, and has certainly never been highlighted in the theatrical versions of any of the X-Men or Wolverine films.
Wolverine (Logan) has had his healing heart broken a number of times, most notably with Jean Grey.
Although it was never depicted in the final cut of any of the films, X-Men star Halle Berry says her character Storm had an intimate relationship with a core member of the mutant team.
In the comics Storm, more informally known as Ororo Munroe, has fallen in love with Black Panther and Forge.