Trump announced last month that he was pulling the US from the global Paris Agreement to combat climate change.
And while Tillerson's predecessor John Kerry stopped off in Paris regularly during his travel, officials in the French capital are finding it hard to set up meetings with the new secretary of state in the Trump administration.
After a photo-op, almost an hour into a tour led by French President Emmanuel Macron, Trump turned to first lady Brigitte Macron.
Mr. Trump was welcomed with all the honors in Paris, where he was invited to commemorate the centenary of the entry of the United States in the First world war. "If it happens", he said, "it will be wonderful; if it doesn't, that will be OK too".
The parade concludes a visit which Mr Macron hoped would boost France's standing on the world stage, despite disagreeing with his American counterpart on policy issues such as climate change.
"We'll see what happens but we'll talk about that over the coming period of time".
Mr Trump praised a ceasefire in southern Syria that he helped broker last week with Russian Federation and Jordan and said the United States was working on a second ceasefire in a "rough part of Syria".
Trump may struggle to stop his mind wondering back to explosive emails in which his oldest son Donald Trump junior appeared to embrace the offer of dirt on Hillary Clinton from Russian interlocutors.More news: Putin would have preferred Hillary to be President, Trump tells Pat Robertson
Objections against Trump's visit to France have so far been muted, with the government insisting on the need to build bridges with the White House and avoid Trump becoming isolated internationally.
Like the Trumps, there is an age difference between the Macrons.
Trump lavished praise on Macron, calling him "a great president", and "tough".
A lawyer for Donald Trump Jr. did not immediately respond to a message seeking comment on whether his client would agree to appear before the committee.
"I think that it is important that we can continue to talk about it", he said through a translator.
"We must work with the government of Iraq to consolidate the gains and ensure the victory stays a victory, unlike last time", he said during the joint news conference. The country is the second largest contributor to the US-led anti-ISIS coalition, a permanent member of the UN Security Council, and a key actor in counterterrorism efforts in northern Africa. France, Trump said, was America's first ally.
Terror attacks in France have killed 239 people in eight attacks since January 2015, with Interior Minister Gerard Collomb saying seven terror plots have been foiled since the start of this year.
"I respect the decision of the president Trump". It's no longer Paris. You have somebody that's going to run this country right.
"A contrast is good", said Daria Bliznets, 28, from Moscow.