French President François Hollande said he condemned Moscow over a treaty signed by President Vladimir Putin on Tuesday that made Crimea part of Russia.
On Tuesday, Putin caused an outcry when he signed a bill for the annexation of Crimea following a controversial referendum in the Ukrainian peninsular on Sunday, which saw almost 97 percent voting to split from Ukraine.
He then told MPs in the Russian parliament that "Crimea was an integral part of Russia."
France, like much of Europe, did not react positively to the Crimea grab.
In a statement from the Elysée Palace, Hollande said it was "against Ukrainian law and international law".
The French president also said that France does not recognise the result of the "illegal" referendum in Crimea on Sunday nor the annexation of this region of Ukraine to Russia.
He called for a "strong and coordinated" EU response to Russia's annexation of Crimea, which he said Paris did not recognise.
"The next European Council on March 20 and 21 must provide the opportunity for a strong and coordinated European response to the new step that has just been taken," he said.
Earlier France's Foreign Minister Laurent Fabius said he "could envisage" blocking a contentious deal to sell two Mistral warships to Russia as a result of Vladimir Putin's stance towards Crimea and the Ukraine crisis.
"If Putin continues what he is doing," then the sale, said to be worth around €1 billion ($1.4 billion) could be off. But that drew an angry response from Russia.
"France is starting to betray the trust we place in it as a reliable supplier," said Russian Deputy Prime Minister Dmitry Rogozin,
Fabius said added that other European countries would also have to impose similar sanctions, notably the UK, but also called for calm over what he said was the biggest crisis in Europe since the end of the Cold War.
"We would ask others, notably Britain to take the same action in regards to the assets of Russian oligarchs in London. Sanctions must be carried out by everyonen" Fabius said, noting that the cancellation of the warships deal, would be bad for France.
"That would be part of the third level of sanctions, but for the moment we are at the second level," Fabius told France's TF1 television.
France has come under pressure over their controversial warship deal since the beginning of the crisis in the Ukraine, but up to now the government has insisted the deal will go ahead as planned.
Earlier this month French President Francois Hollande said sale of two state-of-the art warships was still on course despite Moscow's widely opposed stand over Crimea.
The 2011 sale of the Mistral warships, worth €1 billion ($1.4 billion), was already a deep source of concern for France's NATO and European Union allies, coming only a few years after Russia's invasion of Georgia.
But despite the threat of another war involving Russia, Hollande, who was in Brussels at a European summit on the Ukrainian crisis, said France's commitment to deliver the military vessels was still alive.
"We respect our signed contracts," Hollande said. "We are not yet at that stage and we hope to avoid getting there," he said, referring to the potential of halting the deal.Russian President Vladimir Putin is still invited to D-day commemorations in France on June 6 despite the Ukraine crisis, Fabius said Tuesday.
D-Day invitation still valid
"President Putin has been invited ... and for the moment he remains invited," Fabius said on Europe 1 radio.
Fabius said however he had cancelled a planned trip to Moscow Tuesday with Defence Minister Jean-Yves Le Drian to meet their Russian counterparts.
His ministry earlier said the trip would depend on the "evolving situation" in Ukraine.
"We thought it would be ill-timed, in particular since Mr Putin is due to deliver a speech in the Duma this morning in which he is likely to announce the annexation of Crimea," Fabius said.
A Russian foreign ministry spokeswoman confirmed the talks with Foreign Minister Sergei Lavrov and Defence Minister Sergei Shoigu had been cancelled, saying she was not aware of the reason.