Falcao struck twice before halftime as the hosts set up a rematch of last year’s final against holders Paris St Germain who qualified on Tuesday with a 3-2 win at Stade Rennais.
Rony Lopes was denied a third goal for Monaco after video refereeing ruled the Portugal striker was offside.
Montpellier never really threatened and the principality side comfortably held on for victory.
(Reporting by Julien Pretot, editing by Ed Osmond)
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