Ralph Sutton, 56, from Combe Martin, thought the girls were aged 12 and 13, but they were fake profiles set up by a self-appointed paedophile hunter.
He admitted five charges, including attempting to incite a child to sexual activity, and was jailed for 30 months.
Judge Phillip Wassall said he was "trawling for young girls on the internet".
Sutton was a town councillor in Combe Martin, Devon, where he moved to start a new life after a previous conviction in London in 2010.
The convictions were for downloading indecent images and trying to contact a 14-year-old girl online.
As a result he was subject to a Sexual Harm Prevention Order (SHPO), which banned any internet contact with children.
But he flouted the order by contacting the girls on WhatsApp and messaging service Link, Exeter Crown Court was told.
Sutton suggested meeting the 13-year-old to take her out on his motorcycle and take part in sexual acts.
He was caught by secret vigilante group The Midlands Hunters, who alerted the police.
Warren Robinson, defending, said the offences happened when Sutton was suffering from depression and ill health.
He was fantasising rather than actually trying to arrange face-to-face contact, Mr Robinson said.
Sutton admitted two counts of attempted sexual communication with a child, attempting to incite a child to sexual activity, and two breaches of the SHPO.
Judge Wassall said: "It seems to have been more a question of fuelling your fantasies rather than deliberately intending to exploit the girls directly.
"Nonetheless, this was serious. You gave the clear impression of wanting to meet."
A former councillor who was caught by a vigilante group as he tried to groom two young girls online has been jailed.