If Russia does not accept "deescalation", in particular mediation via a contact group, Thursday's European Council of Ministers' meeting is likely to block visas, take action against the property of 'a certain number of oligarchs" and stop economic talks, Fabius told BFMTV on Wednesday morning.
Lavrov and Kerry, in Paris for a meeting on Lebanon, were due to meet for the first time since pro-Russian forces took control of Crimea, following the formation of a new government in Kiev.
Ukraine's new foreign minister Andrii Dechtchitsa was also due to attend at the hastily organised meeting and met Fabius before it.
The two were in Paris for a meeting on Lebanon, as was Britain's William Hague, but French President François Hollande said on Tuesday evening that the Ukraine crisis was bound to come up.
"Russia has taken the risk of a dangerous escalation," he told the Jewish group, Crif's annual dinner. "In these circumstances, the role of France and Europe is to exercie all the necessary pressure, including sanctions, to find the way to dialogue to find a political solution to the crisis."
Kerry met Germany's Frank-Walter Steinmeier in Switzerland on Monday evening.
Fabius said that France and Germany will put joint proposals to Thursday's European Council of Ministers and France's foreign ministry said Wednesday's meeting was a chance to develop the contact group proposed by German Chancellor Angela Merkel to resolve Ukraine's political crisis.
The Wednesday meeting was organised to discuss the effect of the crisis in Syria on Lebanon, where more than a million refugees are now living.