A subsequent phone call held between the presidents led to the Kremlin signaling a potential for further talks, noting that the leaders had discussed "future contacts in the Normandy Format" - the name given to the diplomatic group of senior representatives of Germany, France, Russia and Ukraine involved in previous peace talks.

Relations between the neighbors remain tense and skirmishes continue but the death of four Ukrainian soldiers in early August prompted new Ukrainian President Volodymyr Zelensky to call for a resumption of peace talks with Russia.

Despite attempts at a ceasefire, both Russia and Ukraine have accused each other of flouting conditions set out in the Minsk peace accords. In total, the armed conflict between separatists and Ukrainian forces in the Donbass has caused as many as 13,000 deaths, according to the United Nations.

Ukraine is of particular importance for Macron given that France and Germany tried to broker a peace deal, known as the Minsk agreements, between Russia and Ukraine following Moscow's annexation of Crimea in 2014. Putin's government is also seen as fomenting a pro-Russian uprising in the Donbass region in the east of Ukraine which led to two areas, Donetsk and Luhansk, declaring themselves as separate republics.

Hosting talks at a presidential residence at the Fort of Brégançon on the Mediterranean coast on Monday, Macron and Putin were expected to talk about the delicate political situations in Ukraine, Libya and Syria.

The meeting between the pair, which comes before the Group of Seven (G-7) industrialized nations attend a summit in Biarritz next weekend, has proved controversial given Russia's turbulent relations with other global powers and Putin's recent crackdown on protesters in his own country.

French President Emmanuel Macron is hosting his Russian counterpart Vladimir Putin for talks on Monday in the hope he can persuade Russia to return to peace talks over Ukraine. The French leader told a press conference following initial talks that he hoped to agree a "Heads of State" summit to discuss Ukraine within weeks.

Russia used to be part of the Group of Eight (G-8) but it was kicked out of the group in 2014 following its annexation of Crimea. Western sanctions on Russia are also in place, causing frosty relations between the country and its neighbor Europe. Russia has retaliated with its own counter-sanctions on agricultural imports from the EU; In June, Putin signed a decree extending the Russian ban on food imports from the EU until the end of 2020.

The lifting of restrictions on Russia's economic activity has been tied to it making progress on its peace agreement with Ukraine.

But experts in Russian foreign policy have little confidence that Macron will be able to persuade Putin to make concessions on Ukraine, although they note that Russia has a vested interest in remaining engaged.

"My sense is that Macron isn't the key interlocutor here. The issue is how Putin shapes up to the new administration in Ukraine and President Zelensky," Daragh McDowell, the principal Russia analyst at Verisk Maplecroft, told CNBC on Monday.

"I wouldn't envisage there will be any concessions on Ukraine at this point. I don't think Putin will want to signal any readiness that he's willing to back down. He doesn't want to signal any weakness to Zelenksy."

Even if peace talks are pushed for by Macron, and the offer taken up by Putin, that is only the start of a process, McDowell noted. "there is some potential for peace talks to reopen but the question is, what would actually be accomplished by those talks?" He added that the situation was something of a no-win one for the Kremlin in that the conflict in Ukraine was a drain on resources but to back down would equate to a loss of face for Russia, particularly among nationalist groups.

AKE Senior Political Risk Analyst Max Hess told CNBC that Moscow "sees the meeting as an opportunity to show that it is not wholly isolated from the international stage."

"However, no progress should be expected in resolving the Ukraine crisis - France does not have the diplomatic capital to get this process going on its own, and it is clear the so-called Normandy Format that also involves Germany is dead, with no meeting under its auspices in the last two years."

"There have been some talk about getting these restarted, which I think is the most success we can hope for. The meeting may see Macron and Putin agree new measures to expand French business in Russia - French energy firm Total has been among the largest Western investors in recent years - but Moscow's agricultural sanctions, which particularly affected France when they were introduced, will not be lifted. The situation in Iran and Syria will be on the table as well, and while it is possible this will include some bilateral efforts to "take the initiative," I also think we are unlikely to get anything game-changing," Hess said.