Kylian Mbappe's double and a last-gasp goal by Christopher Nkunku set up a final showdown against third division Les Herbiers on May 8 at the Stade de France.
PSG, who were crowned Ligue 1 champions on Sunday and won the League Cup, went ahead on 25 minutes when France striker Mbappe scored from close range when he deflected home Edinson Cavani's attempt on goal.
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Caen pushed for an equaliser they got two minutes before the break, Ismael Diomande beating Kevin Trapp with a 20-metre shot.
PSG doubled their tally nine minutes from time as Mbappe latched on to Cavani’s cross.
The visitors sealed the win one minute into stoppage time when Nkunku netted from close range after a neat one-two with Dani Alves.
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