West Jet
Flies into Moncton, NB - 2 hr drive to Freddy Beach

Air Canada
Flies into Fredericton, NB - 15 minutes from downtown Freddy

Via Rail
Stops in Moncton, NB - 2 hr drive to Freddy Beach

Note from Trevor about Via Rail: For the Via info, you can also get off in Mirimichi City and save about an hour or two on the train to Moncton, still about 1.5 hrs to Freddy.  For my test case it was $150 cheaper for two people to get off in Mirimichi than to keep going.  Not sure about how car or bus costs compare out of the two destinations but worth looking into.

Car Rentals

From Airport:
AVIS - 506-446-6006
Budget - 506-446-6123
Hertz - 506-446-9079
Tilden - 506-446-4105