"A number of his ideas, proposals ... are possible as a basis for further steps," Mr Putin said after more than five hours of talks with Mr Macron in the Kremlin.
He did not provide any details but said the two leaders would speak by phone after Mr Macron met with Ukrainian President Volodymyr Zelenskiy on Tuesday.
Mr Putin said he was grateful to Mr Macron for his efforts to solve the security crisis.
"I would like to thank Mr Macron for the efforts France is making to resolve the acute issue of our relations with Nato, to create an environment of stability on the European continent, to resolve the crisis in south-eastern Ukraine," he said.
Mr Putin denied that Russia was acting aggressively towards Ukraine or the West.
"It is not us who are moving towards Nato's borders," he said.
If Ukraine joined the western military alliance, Russia could be pulled into conflict with European countries, Mr Putin said.
"Do you want France to go to war with Russia?" he asked.
The Russian leader said Ukrainian authorities were to blame for the continued conflict the country's east.
"Kiev still rejects every opportunity for a peaceful restoration of its territorial integrity," Mr Putin said.
Mr Macron flew into Moscow at the start of a week of intense western diplomacy aimed at easing fears of a Russian invasion of its pro-western neighbour.
With tens of thousands of Russian troops camped near the Ukrainian border, Mr Macron was the first top western leader to meet Putin since the crisis began in December.
He told Russia to follow him down a diplomatic path and find an "effective response" to Europe's security dilemmas.
Making the first visit to Moscow by a western leader since the Ukraine crisis began, Mr Macron earlier said his talks with Mr Putin could start to sketch out an "effective response, collectively, for Russia and the rest of Europe".
Such a settlement could "avoid war and build bricks of trust, stability and visibility", he said, looking to bridge a political divide symbolised by the oversized Kremlin table that separated the two leaders.
Mr Macron said the discussion could "make a start in the direction in which we need to go, which is towards a de-escalation".
His trip, a politically risky manoeuvre aimed at reviving East-West talks and preventing the stand-off in Ukraine from exploding into war, was the headline act in the intense diplomatic activity on Monday.
The German, Austrian, Czech and Slovak foreign ministers were holding talks in Ukraine before a summit between German Chancellor Olaf Scholz and US President Joe Biden in Washington.
Previous rounds of talks ended with no reduction in the number of Russian troops near Ukraine and the Kremlin unhappy that its demands to curb Nato expansion were not being considered.
But Mr Putin welcomed signals from France that it was open to discussing Moscow's security concerns.
"I see efforts made by the French government, and the president personally, to provide equal security for European players," said Mr Putin. "We've had common concerns in the field of European security."
Such remarks have caused disquiet in Ukraine, where Foreign Minister Dmytro Kuleba voiced concern on Monday about Russia trying to "drive a wedge" between Kiev and its European allies.
Mr Macron had said on the eve of his visit he believed Russia's goal was not to conquer Ukraine but to reset its relations with Nato.
His trip follows three phone calls with Mr Putin in which the Russian leader continued to press for what Moscow calls “security guarantees”.
Mr Macron said his visit, and surrounding diplomatic efforts, could prevent the build-up of more than 100,000 Russian troops from ending in an invasion. US troops landed in Poland on Sunday as Nato tries to deter an attack.
No 'decisive breakthrough' expected
Russia earlier said it was expecting French proposals to reduce the tension but was not anticipating any breakthrough on Monday.
“The situation is too complex to expect decisive breakthroughs in the course of one meeting,” said Kremlin spokesman Dmitry Peskov.
He said it was not possible to speak of a lull in tension while western governments continued to raise the alarm about a potential invasion of Ukraine.
The visit is a political gamble for Mr Macron, who is expected to seek re-election in April but has given the Ukraine crisis as a reason why he has not yet formally entered the campaign.
He spoke to Mr Biden before travelling to Moscow in what Mr Macron’s office said was an attempt to ensure “good co-ordination” with Washington.
US National Security Adviser Jake Sullivan said on Sunday that Russia could invade Ukraine “any day", starting a conflict that would come at an “enormous human cost".
Nato offered a different timeline on Monday, with its most senior military officer Admiral Rob Bauer saying Russia might have enough troops for an invasion by the end of February.
Alliance leaders said Nato was also monitoring Russian movements in Belarus, with an eye on expanding its military presence in the Baltic states and Poland if those troops did not return home after military drills.
"We are considering more longer-term adjustments to our posture, our presence in the eastern part of the alliance," Secretary General Jens Stoltenberg said on Monday.
Russia has denied any plans to attack its neighbour but is demanding that Ukraine and other ex-Soviet countries be banned from joining Nato.
Western powers have rejected this central demand but said they were open to talks with Russia on issues such as arms control.
Mr Scholz visited the White House for his first meeting with Mr Biden since taking office in December.
He repeated the familiar warning from western diplomats that Russia would pay a high price for invading Ukraine.
With Germany’s stance of refusing to supply weapons to Ukraine under scrutiny, Mr Scholz defended Berlin’s record by highlighting its troop presence in Lithuania and its financial support to Ukraine.
But he said diplomacy was bringing results after Germany, France, Russia and Ukraine held talks in a long-shelved grouping called the Normandy format.
“There was not much life there for a long time. We have managed to get that back on track. And that is now the basis for us also talking to each other in Washington,” Mr Scholz said.
UK Foreign Secretary Liz Truss, meanwhile, was expected to visit Eastern Europe later in the week after a positive coronavirus test cancelled her travel plans last week.