The eldest boy among five sons and five daughters, his younger brother Otway Rothwell Falkiner would later rival him as a Merino sheep breeder.
Falkiner was educated at Geelong Church of England Grammar School, and in 1878 the family moved to the Riverina as a result of Otway's asthma.
Franc managed the family properties for some time, and in 1909 became managing director of F.
S.
Falkiner & Sons Ltd on the death of his father.A founding member of Conargo Shire Council (formed in 1906), Falkiner's political interests were awakened by the 1910 Federal land tax, which prompted him to enter the Australian House of Representatives.
He won the seat of Riverina in 1913, representing the Commonwealth Liberal Party, but lost it to the former member, John Chanter, the following year.
He won Hume in 1917 for the Nationalist Party, but was defeated in his attempt to transfer to the Senate in 1919.