Speaking earlier on Tuesday, DUP leader Arlene Foster told reporters that discussions centered on "bringing stability to the United Kingdom government in and around issues around Brexit, obviously around counter-terrorism, and then doing what's right for Northern Ireland in respect of economic matters".
As May attempts to cobble together a majority, the EU's chief Brexit negotiator Michel Barnier warned that time was passing in an interview on Tuesday.
Many in Northern Ireland, especially the Loyalist community, see this DUP-Conservative arrangement as a good thing if the deal is signed today, as it may highlight the areas of Northern Ireland that need investment.
The DUP leader said: "There's been a lot of commentary around the issues that we are talking about and it won't surprise anyone that we are talking about matters that pertain, of course, to the nation generally".
Prime Minister Theresa May did not receive an overall majority and is in talks with the Democratic Unionist Party over a deal to prop up her government.
Macron said the door was "always open" for Britain to remain in the European Union as long as the negotiations on Brexit have not finished.
Although there are likely to be some tensions between the Conservatives and the DUP, the two parties have now agreed broad consensus that will give May just enough room to run a government, although nothing like the way she wanted when she called the snap election.
It follows warnings - including from former prime minister Sir John Major - that the Government will compromise its stated impartiality in the province if it enters a confidence and supply deal with the DUP at Westminster.
"My main concern is the peace process", he said.
Jeremy Corbyn, leader of the opposition Labour Party, which saw its number of parliamentary seats and share of the vote increase, said there could be another election this year or early in 2018. She also signalled she's willing to rethink her approach to Brexit.
The Irish republican Sinn Fein party - which won seven seats in the election, although their MPs traditionally do not take up their seats in protest - is also wary of the alliance.
While the DUP are deeply eurosceptic, they have baulked at the potential loss of a "frictionless border" with the Republic of Ireland.
Brussels, The European Union (EU) and the European Commission (EC) said in a joint statement that they have set a date to begin Brexit talks with the UK.
She will have to manage conflicting demands from within her own party, including a proposal for business groups and lawmakers from all parties to agree to a national position for Britain's most complex negotiations since World War Two.