The sentence comes two years after the pair were banned from Luton and attending any mosque in the country after a successful High Court injuction by Beds Police.
Appearing at Folkestone Magistrates' Court, Fransen was convicted of three counts of religiously-aggravated harassment and Golding convicted of one count.
He said their words and actions "demonstrated hostility" towards Muslims and the Muslim faith.
Videos had been posted online in which Fransen claimed to be exposing four offenders who were on trial at the time for raping a teenage girl at a flat in Northwood Road, Ramsgate.
"The fact that completely innocent members of the public were accused of being rapists, making them fear for their own safety, shows how little regard they have for the consequences of their actions".
Leader of Britain First Paul Golding (right) with deputy leader Jayda Fransen (left).
They filmed themselves targeting people they believed were connected to that case and released the videos on social media and the party's website.
He told the court the pair were "well-known", "controversial" and "generate their own publicity", but his verdict was based "solely on admissible evidence heard in court".
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The defendants also posted offensive leaflets through letterboxes of houses close to where they thought the alleged rapists lived.
Judge Justin Barron, jailing Fransen for 36 weeks for three charges and Golding for 18 weeks for one charge, said the crimes were "deliberately planned against targeted victims".
She was convicted of abuse after visiting a house she wrongly believed to be the current address of another defendant, Sershah Muslimyar.
"These defendants were not merely exercising their right to free speech but were instead aiming religiously aggravated abuse at innocent members of the public", said the chief crown prosecutor, Jaswant K. Narwal.
In the few months since, however, the only thing that seems to have risen is the number of court rulings against Fransen and her Britain First colleague.
Britain First has been noted for its extreme white supremacist and anti-Muslim stance in the past and Fransen, its deputy leader, gained particular notoriety when racially charged videos she published on Twitter were retweeted by Donald Trump.
The Finsbury Park terror attacker, Darren Osborne, read Britain First posts before his attempted massacre of Muslim worshippers, while neo-Nazi Thomas Mair repeatedly shouted the group's name while murdering Labour MP Jo Cox.