• Johnson and prominent members of his ruling Conservative Party have publicly called for the scrapping or radical overhaul of the Northern Ireland Protocol.
• The Protocol came into force last year and was designed to prevent customs checks and an effective land border between Northern Ireland, which is part of the U.K., and the Republic of Ireland, which remains in the EU.

LONDON — U.K. Prime Minister Boris Johnson must respect every aspect of the Brexit withdrawal agreements, former European Union Chief Negotiator Michel Barnier has urged.

Johnson and prominent members of his ruling Conservative Party have publicly called for the scrapping or radical overhaul of the Northern Ireland Protocol, a portion of the withdrawal agreements negotiated by the U.K. and the EU in 2019.

The protocol came into force last year and was designed to prevent customs checks and an effective land border between Northern Ireland, which is part of the U.K., and the Republic of Ireland, which remains in the EU. This is particularly important given the fragile peace in Northern Ireland since the Good Friday Agreement of 1998.

However, the protocol requires checks on goods traveling into Northern Ireland from the rest of the U.K., and has caused uproar among Northern Ireland's unionists who claim it poses a threat to the country's place within the U.K.

British Foreign Secretary Liz Truss and European Commission Vice-President Maroš Šefčovič met in London on Friday for talks, but the impasse between London and Brussels shows little sign of abating.

The U.K. government has also bemoaned the bilateral agreement on fisheries contained within the Withdrawal Agreement, with the British fishing industry struggling to navigate post-Brexit license disputes.

Speaking to CNBC exclusively on Monday ahead of the French presidential elections, in which he is supporting center-right Les Republicains candidate Valérie Pécresse, Barnier said the British prime minister would need to honor agreements made with the European Union in order to preserve relations between the U.K. and France.

"The commitments made by Mr. Johnson in the Brexit negotiation — in the first pact we negotiated, which includes the Ireland protocol, and the issue there is that of peace in Ireland, the stability of the island, and the second pact on Brexit's trade and industry where the fisheries treaty is found — these two pacts that have been negotiated step by step, comma by comma, sentence by sentence by Mr. Johnson, and that he knows very well, must be respected, that the U.K. maintain its commitments with regard to the European Union, with regard to France," Barnier told CNBC's Charlotte Reed.

Despite differences over the existing agreements, however, he suggested that it is more important to "look ahead to the future" as far as relations between London and Paris are concerned.

"We have many reasons to work together, not only on a military scale, against terrorism, climate change, transborder cooperation, there are many reasons why France and the U.K. should greatly cooperate."