Twice.
The University of Florida made it to its first NCAA men's Basketball Final Four in 1994. In its second Final Four (2000), the team lost the title game to Michigan State 89-76. In 2006 and 2007, Florida won the tournament, becoming only the second school to win back-to-back titles since UCLA's consecutive wins in the 1960's and '70's.
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The NCAA does not award a national title in College Football at the Division I-FBS/Division I-A level.
National championships are instead awarded by outside agencies, such as the Associated Press or the American Football Coaches Association.
Florida currently claims three of those titles (1996, 2006, 2008).
The Florida Gators have claimed national titles 3 in Football (1996, 2006, and 2008).
FSU played for the National Championship in 1972, so I would say that it was in the final two. So yes.