Writing on X, the president's chief of staff Paweł Szefernaker said the talks covered the future of Europe, security and the role of sovereign states within the EU.
He described it as a "very good conversation" and pointed to the shared challenges and opportunities for cooperation between Poland and France.
Earlier the same day, Bardella visited Poland's parliament, the Sejm, where he met members of the far-right Confederation party, including deputy speaker Krzysztof Bosak.
According to news outlet Politico, the Warsaw visit forms part of a wider European tour by Bardella as he seeks to build alliances ahead of a potential French presidential bid next year.
Bardella is widely expected to stand as the National Rally's candidate if party leader Marine Le Pen is barred from running, following a court ruling due in early July.
His trip comes after the grouping lost its most high-profile ally in the EU, when former Hungarian Prime Minister Viktor Orbán was defeated at the polls earlier this year.
In an interview with Politico published on Monday, Bardella was asked why he chose to visit Poland.
He said it was "a country that counts, and each day it counts a little more on the European stage."
Bardella noted that Poland is now the EU's sixth-largest economy and has made clear commitments in recent years to defend its borders against migration pressures.
He added that, in seeking greater strategic autonomy, "Poland has been making very clear efforts in terms of rearmament and defense."
(ał)
Source: Politico, PAP