"The European Union can not forever be hostage to the resolution of a political crisis in the United Kingdom", he said.
He again warned that the Brexit Withdrawal Agreement is the only deal on the table - and said that if the UK Parliament fails to pass it in the coming days, the country will have to request a longer extension or face leaving without a deal.
Leo Varadkar held Brexit talks with Macron this afternoon as efforts intensify to find a solution to the current impasse, while German chancellor Angela Merkel is due to meet Varadkar in Dublin on Thursday to discuss no-deal preparations.
"We will never abandon Ireland or the Irish people no matter what happens, because this solidarity is the very goal of the European project", said Mr Macron.
Irish prime minister Leo Varadkar said on Tuesday that the European Union should be open to "any proposals" that United Kingdom prime minister Theresa May might bring forward to resolve the Brexit impasse.
Mr Coveney added that in the case of a no-deal Ireland will have a dual obligation to manage the border issues and also protect the integrity of the European Union single market.
But as well as Irish commitments to the EU, Varadkar said Ireland had to honour the 1998 Good Friday Agreement that ended sectarian conflict on the island of Ireland.More news: Fernando Alonso - Bahrain test not a precursor to full F1 comeback
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Macron met Varadkar, the Irish taoiseach, to discuss no-deal plans for the Irish border as well as how to handle any extension request from Theresa May.
"We've set out clearly to Mr Barnier and others that any hardening of that border would represent a step backwards for Ireland".
Mairead McGuinness, vice-president of the European Parliament and Fine Gael MEP, said that a no deal does not solve problems for those that would advocate for a hard Brexit.
This morning, chief European Union negotiator Michel Barnier warned that a no-deal scenario was becoming more likely by the day. "We need to be open to any proposals that she may bring forward to us", adding that as things stood Britain was heading towards a no-deal exit.
The Tánaiste also warned that Ireland will not tolerate a situation where mainland European Union states impose controls on Irish exports.
Mr Varadkar has consistently warned that the United Kingdom will have to accept Northern Ireland being treated differently to Britain on customs and regulations if it is to keep its promises that Brexit will not lead to a hard border.
He said his government was now in negotiations with the European Commission as to how to achieve both of these objectives.