Train drivers and other staff launched the first strikes on April 3 as part of three months of planned stoppages in a bid to force Macron to back down on plans for an overhaul of the heavily indebted state rail operator SNCF.
In Russia, Syria's main military ally, kremlin spokesman Dmitry Peskov warned against "any steps, which could lead to an escalation of tensions".
Macron added that Russian Federation, which backs Assad politically and militarily, had made itself complicit in the Syrian government's actions.
Both Putin and Rouhani agreed the missiles strikes had "seriously damaged" the prospect for a political settlement in Syria, the statement said. The Western states put the blame of the attack on Damascus, while the Syrian forces firmly denied the claims.
The Organization for the Prohibition of Chemical Weapons, an worldwide chemical weapons watchdog organization said Thursday that its team is en route to Syria and will begin work Saturday to investigate the attack.
"This action was proportionate and targeted, it was not aimed at (Syrian President Bashar al) Assad's allies nor at the civilian population", Le Drian said in a televised statement.
That acknowledged that Syria had crossed a red line that Mr Macron set a year ago promising French military action if the use of gas was confirmed.
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"The president of the Republic said he wanted the dialogue between France and Russian Federation to continue and intensify in order to bring peace and stability to Syria", the French presidency said after the call, which came as the West ponders possible strikes on Syria in retaliation for a suspected chemical attack.
At the same time, Macron is trying to reinforce France's position as an enforcer of worldwide treaties, which includes the Chemical Weapons Convention that 192 countries have signed.
"The tone was very direct, the two presidents were under no illusion about what was going to happen", the advisor told Reuters on Saturday, soon after the overnight air strikes.
For the moment, public opinion polls in France suggest that a plurality of citizens are skeptical of carrying out a strike on Syria.
The decision to strike Syrian government targets followed a week of hectic diplomacy and coordination with USA and British allies. Syria's official SANA news agency reported.
The Syrian president added that the threats endanger worldwide peace and security and that military action would only contribute to the "further destabilization" of the region.