Northern Irish political leaders including the Sinn Fein president Gerry Adams will meet with Theresa May on Thursday to discuss plans for a deal between the Conservatives and the Democratic Unionist Party that critics claim will undermine the peace process.
Foster added: "I know people want to talk about soft Brexit, hard Brexit, all of these sorts of things, but what we want to see is a sensible Brexit and one that works for everybody".
The Conservatives unexpectedly lost their parliamentary majority in last week's general election, which May called in order to strengthen the party's mandate heading into the discussions with European Union leaders.
Ms May is now engaged in talks with the Democratic Unionist Party in Northern Ireland over a so-called "confidence and supply" arrangement that will give the Conservatives a majority in the House of Commons and the ability to form a government.
She said: "I want to ensure that we can look again at issues like Brexit which we know we are now going to have to get cross-party support for".
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.
"Going overseas and being seen to be the prime minister and talking to the president of France, being seen to be wheeler-dealing on the worldwide stage, is a classic move to shore up authority at home", he told AFP.
The DUP's consent to the announcement of a date for a delayed Queen's Speech is a sign that they have agreed the first part of this deal.
"I think there is a unity of objective among people in the United Kingdom", May said following a meeting with French President Emmanuel Macron on Tuesday.More news: Top 3 miss US Open cut; 4-way tie for 1st
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Talks between the two parties continued today amid reports any announcement of a deal may now be postponed because of the tragic fire.
European Union leaders have voiced growing impatience to start Brexit negotiations, which have already been delayed by the parliamentary election - and on which the clock is ticking.
Devolved government in Northern Ireland broke down in January.
Arlene Foster says she hopes to conclude the talks soon.
Downing Street sources told our correspondent talk of a delay in announcing a deal was "not coming from us".
Though on the surface, Thursday's meeting with Northern Irish parties is aimed at breaking the logjam in forming a new cross-party regional government in the province, May needs broader acceptance of a Conservative-DUP deal.
The EU's chief Brexit negotiator Michel Barnier also warned Tuesday that time was passing.
What has Theresa May said?
But the prospect of a deal has caused consternation in Dublin, with Ireland's outgoing premier Enda Kenny warning that such an alliance could upset Northern Ireland's fragile peace.