An initial round of talks between May and DUP leader Arlene Foster ended with no agreement on Tuesday.
"We have seen in Northern Ireland over very many years that events always don't unwind as you expect them to unwind", he said.
Without a confidence and supply deal with the DUP, the Tories risk losing the vote next week on the Queen's Speech, which lays out the agenda for the government.
The talks with the DUP follow her apology to Conservative rank-and-file lawmakers in a meeting for the party's poor election result.
"Delay to deal with DUP means likely postponement of Queens speech; and possibly Brexit talks", BBC political reporter Norman Smith said on Twitter.
DUP leader Arlene Foster, who travelled to Westminster for talks with the Tories on Tuesday, said she hoped a deal could be reached "sooner rather than later".
While the DUP are deeply eurosceptic, they have baulked at some of the practical implications of a so-call hard Brexit - including a potential loss of a "frictionless border" with the Republic of Ireland - and talks will touch on efforts to minimise the potential damage to Northern Ireland.
Barnier held "talks about talks" with May's Brexit advisor Olly Robbins and British EU Ambassador Tim Barrow in Brussels on Monday but they failed to agree on a date for the negotiations to begin, an EU official said.
Gigaba announces plans for further budget cuts
Inclusive growth and economic transformation are the top priorities of the government, and are mutually reinforcing, Gigaba said.
Downing Street said Cabinet ministers had discussed the Government's legislative programme when they met earlier but refused to be drawn on discussions about plans to deal with the DUP.
LibDem leader Tim Farron said this was because in the last parliament none of the party's eight MPs were women "and we didn't feel it was right to elect a deputy in those circumstances".
Instead she finds herself weakened and isolated as she meets Macron, a 39-year-old neophyte who rode to victory in last month's presidential elections and is on course for a landslide victory in France's legislature.
It is thought Mrs Foster, despite being a Brexit supporter, could seek assurances from Mrs May that she will pursue a softer exit from the European Union, given Northern Ireland's 56% Remain vote and the DUP's desire not to see a return to a hard border with Ireland.
Even the idea of an alliance is complicated, however.
Sinn Fein's Stormont leader Michelle O'Neill said: "I will be making it very clear that any deal between the Tories and the DUP can not be allowed to undermine the Good Friday and subsequent agreements".
The 1998 Good Friday Agreement - also referred to as the Belfast Agreement - commits the United Kingdom and Irish Governments to demonstrate "rigorous impartiality" in their dealings with the different political traditions in Northern Ireland.
Meanwhile, the chief European Union negotiator has told the Financial Times that the clock is ticking on Brexit talks, and that Britain should be wary of further delays.
"My preoccupation is that time is passing, it is passing quicker than anyone believes because the subjects we have to deal with are extraordinarily complex..." When asked about the Daily Telegraph article, Michael Gove, a minister who campaigned for Brexit, told ITV: "This is news to me".