The two met in the Kremlin on Friday and “were on the same wavelength”, according to one of Ms Le Pen’s aides, Ludovic de Danne.
“We felt they understood each other, ” he said.
The 90-minute meeting focused on global issues such as terrorism but very little was said about next month’s election in France, Mr de Danne added.
Ms Le Pen has visited Russia many times, although this was her first meeting with Mr Putin.
She has previously called for closer ties with the Russian leader and approved of Moscow’s annexation of Crimea in 2014.
After the meeting she said that one of her first actions if she wins will be to look at “swiftly” ending European Union sanctions imposed on Russia over the Ukraine crisis.
Speaking to reporters at a Moscow hotel, Ms Le Pen also denied discussing financial support for her party and said she was not meeting Putin an attempt to boost her chances in the election.
“He represents a sovereign nation,” Ms Le Pen said. “I think he also represents a new vision.
“A new world has emerged in the past years. This is Vladimir Putin’s world, Donald Trump’s world in the United States, Mr (Narendra) Modi’s world in India.”
Mr Putin said: “We by no means want to influence the current events but we reserve the right to communicate with all representatives of all political forces of the country, as do our partners in Europe and the United States, for example.
“I know that you represent quite a fast-developing spectrum of European political forces.”
Kremlin spokesman Dmitry Peskov said: “Russia is ready to stay in contact with representatives of all political forces, with the current leadership, with representatives of the opposition.”
He added it was “important” for Moscow to exchange with political forces that advocate “the need to engage in bilateral dialogue to find solutions to existing problems”.
Last week, Ms Le Pen’s rival and presidential favourite Emmanuel Macron met German Chancellor Angela Merkel in Berlin.
Mr de Danne said the Berlin meeting and the Moscow meeting were different because “Macron-Merkel it’s the declining establishment, Le Pen and Putin represent the freedom of the people, cooperation in a multi-polar world”.