Barnier promised to help the Republic avoid a return to a hard border with Northern Ireland after Brexit, but said the UK's departure from the European Union would have consequences for customs controls.
He said: 'We want these negotiations to succeed. "Still no coffee but a bit more - a little bit more - seat space than before".
Ibec CEO Danny McCoy will stress the need for a range of key Irish concerns to be directly and explicitly addressed in exit negotiations and in the terms of a future EU-UK trade deal.
"I am fully aware that some member states will be more affected than others", Michel Barnier said in an address to both houses of the Irish parliament, an honour usually only reserved for visiting heads of state.More news: Fox harassment claims create clouds around Sky takeover bid
Even as Barnier offered reassurances to his audience, he underlined the challenge at hand.
"If we put things in the right order, if we negotiate with mutual respect, without any kind of aggressivity... and if we are open to finding solutions, there is no reason why our strong Europe can not maintain a strong relationship with the UK", Barnier said.
Mr Barnier - who has previously served as a European Commissioner and held various French cabinet positions - will hold a private meeting with Enda Kenny after addressing a special joint sitting of the Dáil and Seanad this morning.
Mrs May has accused Brussels insiders of seeking to influence the outcome of the June 8 General Election.More news: Antonio Conte calls for 'one more small step' after Chelsea beat Middlesbrough
Mr Barnier said: 'if we put things in the right order, if we negotiate with mutual respect, without any kind of aggressivity. if we are open to finding solutions, there is no reason why a strong Europe can not maintain a strong relationship with the United Kingdom'.
For Brexit, emphatically driven by a cadre of long-standing Eurosceptic English Conservative MPs, is challenging the very survival of the United Kingdom, with Scotland engaged in an unprecedented constitutional confrontation with the London Government, and Dublin perturbed about the implications for Northern Ireland.
Talks on a "bold and ambitious but fair free-trade agreement" could only begin once progress has been made on issues including the UK's divorce bill.
"We have to use our combined strength", he said, "and deliver solutions that benefit all member-states".More news: Kellyanne Conway says James Comey's own actions led to his firing