Is there any evidence of Fox and Marvel coming to an agreement for characters from both the Marvel Cinematic Universe and the X-Men franchise to appear in each other's films? If not, when does Fox's license on the X-Men run out?
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Here is some info, although I don't know how reliable it is:
While the above forum post may not be what is usually considered a "reliable source", about a year and a half ago it was announced that Daredevil might go back to Marvel:
Last summer, Marvel got the rights on Daredevil back (source).
To me, this confirms the above "they have rights as long as they make the movies (which, in practice, means as long as it's profitable to make them)".
As @VedranŠego's answer says, Fox owns X-men right till they make movie on them. Fox already have lost right of Daredevil and related property, so they are not seen interested in loosing anymore rights of marvel character.
Some rumors suggest Fox has to use this property and make film in every 3-4 year too sustain rights. And currently, Fox didn't stopped making film on X-Men character because they have a milking cow and didn't want to loose it.
X-Men: Days of Future Past is coming this year and X-Men: Apocalypse, X-Force and The Wolverine sequel are in development. There might be a plan for Deadpool Film but no update have been given since 2011.
There is also a plan of reboot for Fantastic Four film, which will share continuity with X-men to make a Shared universe like Marvel's Avenger.(source)
So it looks like Fox is not going to loose rights soon and after the The Quicksilver Controversy, Fox and Marvel is not showing any intention for friendly relation and having different version of same character will going to make thing more complex for crossover.