With a chaotic exit of Britain from the European Union potentially only days away, EU commissioner Phil Hogan says that the United Kingdom leaving the bloc without a deal in place "is simply insane".
Mr Barnier's visit is the latest evidence of intensifying diplomatic exchanges between the Dublin government and key European Union figures in the Brexit process.
He said "our goal is to protect the Good Friday Agreement, peace on this island and integrity of the single market".
He reiterated that, although he wishes to see a deal ratified, contingency planning for a no-deal Brexit has intensified in Ireland, and that Ireland would be open to an extension.
One thing is certain, whatever happens, the European Union will stand fully behind Ireland.
At the weekend, Mr Varadkar said his own preference was for a longer extension than the June 30 date proposed by the UK.
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Varadkar said: "There will be different views but I am confident that we will reach agreement".
Macron is not happy with that permissive approach and is seeking a further "backstop" to any deal with May that would entail a further summit once it was clearer whether early ratification or a British EU election were happening or not.
"There have been intensive discussions between our teams over the past (few) weeks", he said.
The British government is now in talks with the opposition Labour Party on a possible compromise that could include a customs union.
Therefore, the former French Foreign Minister warned that if a no-deal Brexit results, London and Brussels would not open negotiations on their future trade relationship as long as the future of the Irish border is not resolved first.
Meanwhile, Mr Macron stressed: "We will never abandon Ireland or the Irish people no matter what happens, because this solidarity is the very objective of the European project".
In light of recent reports of Spain and France's harsh conditions on any kind of extension, Mr Varadkar said he believes it is "very unlikely" that one of the European Union 27 states will refuse Mrs May's request of a deal extension.
The Taoiseach also had a phone call with Prime Minister May this evening, who spoke about her recent letter to Donald Tusk seeking an extension of the Article 50 deadline, and her ongoing preparations for the Summit on Wednesday.