Clement Beaune, France’s European Affairs Minister, shared a mock cartoon of the two officials on Twitter. The drawing depicts Mr Beaune dangling a pen on a fishing rod infront of the UK’s former EU negotiator.
In the satirical post, it adds: “It would be good to put the ink away.”
It comes as the France and UK remain locked in a row over post-Brexit fishing rights.
Mr Beaune accompanied the tweet by calling on London to “rebuild a climate of trust” with Paris.
He wrote: “We had difficult relations, but we always continued the dialogue. I greet with respect David Frost after his resignation.
Relations between the UK and France have been strained ever since Brexit came into force in January.
A huge row erupted at the start of the year after France blocked UK lorries from crossing the Channel amid fears over the so-called Kent variant of Covid.
Further flashpoints have sparked over the supply of vaccines from Europe, licences for French fishing boats and the migrant crisis in Calais.
On Friday, Mr Beaune stoked tensions further by asking the European Commission to look into taking legal action against the UK over the fishing spat.
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He confirmed French fishermen had obtained 93 percent of the licences it has applied for.
Maritime Minister Annick Girardin said 73 applications were still outstanding.
Mr Beaune said: "The next step will be to ask the Commission in the coming days to convene the Partnership Council as provided for under the Brexit trade deal to settle a problem.”
The 40-year-old added: “We will ask the Commission in the coming days to start litigation to obtain the licences we are entitled to.”
The UK has approved more than 1,000 licences to enable French vessels to fish in British waters.
The Government said licences would continue to be issued in line with the Trade and Co-operation Agreement (TCA) signed last December.
A spokesperson said: "Our approach to licensing has been reasonable and entirely in line with the TCA We have licensed vessels where sufficient evidence has been provided to demonstrate they qualify for access under the TCA.
“Where that evidence has not been provided, licences have not been issued."