On Monday, Boris Johnson, Britain’s new foreign secretary, was also making his debut at a meeting of EU foreign ministers in Brussels.
Mrs May’s relationship with Ms Merkel will be crucial in the coming months. The German leader has urged patience with the UK in the face of demands from other EU members states, including France, that Britain should trigger Article 50, the so-called EU divorce clause, as soon as possible.
But the German chancellor has also taken a tough stance on any Brexit negotiations, warning the UK that if it wants to retain access to the single market it will have to accept freedom of movement.
Mrs May’s trip to Paris is likely to be even more testing, with Mr Hollande wanting to make the UK pay for Brexit. He is under pressure domestically ahead of elections next year where membership of the EU is already one of the central issues of the campaign.
Marine Le Pen, leader of the National Front, who is almost certain to qualify for the second round of the presidential election, is set to campaign for Frexit — a French exit from the EU.
But security issues will also be high up the agenda in Paris following the Nice atrocities. The UK and France enjoy a strong bilateral relationship in this area as well as on wider defence issues.
Mrs May met Wales’ first minister Carwyn Jones in Cardiff on Monday morning meeting as she sent out a clear message that she wanted the principality “involved and engaged” in Brexit negotiations.
The visit underlined Mrs May’s position made clear at the end of last week, during a visit to Edinburgh to see Scottish first minister Nicola Sturgeon, that she would prioritise keeping the UK together over a swift exit from the EU.
After the meeting, Ms Sturgeon signalled there may be a way to keep Scotland in both the UK and EU having previously said a second independence referendum north of the border was “highly likely” if Brexit went ahead.
A spokesman for Mrs May said: “On Wednesday, following Prime Minister’s Questions, she will travel to Berlin for a bilateral meeting and a working dinner with chancellor Merkel.
This will be an opportunity to discuss the bilateral relationship, co-operation on a range of global challenges, and of course how the UK and Germany can work together as the UK prepares to leave the EU.”
Downing Street added: “Then on Thursday, the Prime Minister will visit France for a bilateral meeting with President Hollande at the Elysée. The talks are likely to cover similar issues as those in Berlin, as well as Thursday’s attack in Nice and counter-terrorism co-operation.”