May should be able to use these two set-piece events to shape the country's future.
Irish Prime Minister Enda Kenny has sought assurances from Mrs May that "nothing should happen" to endanger the Good Friday Agreement.
He said the industry organisation had always supported a "pragmatic" approach to the challenges of Brexit, and said the government had (in principle) pledged to support its calls for a "free and frictionless" border and open access to talent in highly skilled industries, such as pharma.
"Northern Ireland's political leaders now have this chance to take control and restore effective power sharing government under the current assembly mandate".
The Conservatives won the biggest share of seats in Thursday's election, but lost their majority in Parliament and will have to rely on support from a smaller party to govern.
The European Union's executive arm has indicated that negotiations with the British government over the country's exit from the bloc may not start next week as planned. "We're not going to have a soft or a hard Brexit".
"Overall, we believe that the election outcome will hamper Brexit negotiations and increase fiscal risks, and therefore be negative for the U.K.'s credit profile", Moody's said in a statement. "This doesn't depend entirely on us".
Theresa May told Conservative lawmakers on Monday she would serve as Prime Minister as long as they wanted her after a botched election gamble cost the party its majority in parliament and weakened Britain's hand days before formal Brexit negotiations.
May says there will be no second general election.
Sinn Fein leader in Northern Ireland Michelle O'Neill arrives at a polling station at St Patrick's primary school in Annaghmore Clonoe
The PM's spokesman told reporters it was not for him to confirm the date - which has been in the Queen's diary since April - and that new Leader of the Commons Andrea Leadsom would be providing an "update" shortly.
Labour and the Conservatives agreed before the election that Brexit must mean leaving the single market, but last week's result has emboldened those at Westminster who favour temporary membership of the European Economic Area (EEA) as a transitional arrangement after Britain leaves the EU.
David Davis, the cabinet member in charge of Brexit, said talks with the European Union may not start on Monday as planned because it would clash with the scheduled date of the Queen's Speech.
"Going overseas and being seen to be the prime minister and talking to the president of France... is a classic move to shore up authority at home", said Colin Talbot, professor of government at the University of Manchester.
However, Mrs May assured MPs the DUP would not have any sway over policy on LGBT rights and any "confidence and supply" deal with them would not have any effect on talks aiming to restore the power-sharing Northern Ireland Government.
However, there is no agreement about when she should stand down, and Tory MPs are concerned that if she does so now, there will be pressure for a second election after a leadership contest - since the victor will have no mandate to govern as Prime Minister (or so it will be argued).
May's Conservatives unexpectedly lost their majority in parliament in snap vote, causing political chaos ahead of Brexit talks with EU.
Nicky Morgan, the former education secretary, said: "I think it is fairly clear that Theresa May can not lead us into another election, obviously we don't know when that is going to happen".