French President Emmanuel Macron has invited Donald Trump to next month's Bastille Day celebration, marking a century since the arrival of US troops to Europe during the First World War.
The invitation to the US President and First Lady Melania Trump was extended during a telephone conversation between the two leaders on Tuesday (27 June).
Macron's office said the White House is examining the feasibility of a Paris visit.
France celebrates Bastille Day with a military parade down the Champs-Elysees every year on 14 July.
Security is expected to be tight in Paris and at other events across the country after last year's Bastille Day celebrations in Nice were marred by an Islamist terrorist attack.
Tunisian-born Mohamed Lahouaiej Bouhlel intentionally drove a truck through crowds on the Promenade des Anglais, killing 86 and injuring hundreds more.
Presidents Macron and Trump met face-to-face for the first time during the Nato summit last month, engaging in an awkward white-knuckle handshake for which Trump has become infamous.
The pair have not seen eye-to-eye on every issue, with the French leader mocking Trump's subsequent decision to pull the US out of the 2015 Paris Agreement to combat climate change, calling it a "mistake" and adopting the Trump-style slogan "Make our planet great again".
France's foreign ministry also issued a video debunking some claims the White House had made on the Paris Agreement.
During Tuesday's White House press briefing, a reporter asked Energy Secretary Rick Perry if he thought Macron's Bastille Day invitation signalled a thaw in tensions between the two countries.
"Do you see this as a way that the French are taking up his suggestion for negotiating a new climate change agreement?" the reporter asked.
"I would always look at an invitation to a party as a good thing," Perry said to laughter.
Trump and Macron's phone call on Tuesday was in preparation for the G20 summit in Germany on 7 July.
As well as a possible Bastille Day visit, the pair discussed the need for a joint response in case of a chemical attack in Syria.
The Pentagon earlier in the week warned that US intelligence had noticed suspect activity at the launch site of the regime's apparent chemical strike in April.
Days after that strike on a rebel-held town, the US launched a cruise missile strike on an airfield used by the Syrian regime.
The French foreign ministry has not revealed if it has similar intelligence on a further chemical attack being prepared.
But following a meeting last month with Russian President Vladimir Putin, an ally of the Syrian regime, Macron drew a "very clear red line" on the use of chemical weapons and warned of reprisals against "whomever" responsible.