Mineur was convicted in an earlier court appearance at Preston Crown Court of making and possessing indecent images of children.
He was elected as a Conservative councillor for Greenlands Ward in 2007 but lost his seat in 2011.
The court heard police found indecent images of children on his computer following searches of addresses on Sackville Avenue, Blackpool in December 2010 and on Common Edge Road in August 2011.
The images included Level Five, the most serious category.
Brett Gerrity, senior crown prosecutor for Crown Prosecution Service North West, said: "Since his first appearance in court in July 2012, Julian Mineur continuously denied that he had ever knowingly viewed or downloaded indecent images of children. As a result of his evasive actions, and at an increased cost to the public purse, several computer expert reports were completed which provided overwhelming evidence to show that he had indeed accessed such images on a number of computers that belonged to him."
Mineur, who was ordered to pay £1,000 costs, was elected as a Conservative in 2007 but subsequently deselected by the party, fighting the 2011 election as an independent.
Julian Mineur, 59 at the time of his trial, of Common Edge Road, Blackpool, was given a three-year community order and placed on the sex offenders register for 10 years.
Julian Mineur failed to notify police that he held a Vanquis credit card while living at farm cottages near Duns, between February and December. The 60-year-old, now living in Prince’s Street in Lockerbie, was placed on the sex offenders register last March which required him to notify police within three days of all financial accounts held by him.
Defence lawyer Maureen Sinclair said the offence had been caused by a "Misunderstanding" and said her client apologised for the error.
Sheriff Kevin Drummond accepted it was an "Administrative" offence but said he would mark the breach with a fine reduced from £150 due to the guilty plea.
Mineur was convicted earlier this year at Preston Crown Court of having images of child sex abuse on his computer. He was given a three three-year community order and placed on the sex offenders register for 10 years. The court heard police found indecent images of children on his computer following searches of addresses on Sackville Avenue, Blackpool, in December 2010 and on Common Edge Road in August 2011. The images included level five, the most serious category. Mineur, who was also ordered to pay £1,000 costs, was elected as a Conservative councillor in Blackpool in 2007 but subsequently deselected by the party, fighting the 2011 election as an independent.
Mineur, a former Conservative Councillor who breached the terms of the Sexual Offences Act was fined £100 at Jedburgh Sheriff Court.