In a letter to German Chancellor Angela Merkel - the architect of the pact, which aims to tighten budgetary discipline in Europe - the Greens welcomed an Italian proposal to ratify the text simultaneously as a "European signal."
"We suggest you also synchronise with France and propose this to the newly elected French president," the Greens wrote.
"The Franco-German friendship was and is the motor of European integration. Close cooperation on this topic seems to us to be particularly important," the letter concluded.
Last week, Merkel's spokesman said the chancellor would welcome a simultaneous ratification in Italy and Germany.
The centre-left Social Democrats (SPD), Merkel's main opponents, also called for a joint ratification.
"Joint action in France and Germany would be very welcome," Michael Roth, the SPD's spokesman on European affairs, told news agency AFP.
Merkel needs a two-thirds majority in parliament to pass the fiscal pact, which she signed in March, and therefore needs opposition support.
The SPD has echoed calls from French President-elect Francois Hollande to place more emphasis on growth in the fiscal pact.
Negotiations in Germany over the text were due to begin next week.
The government wants the ratification to take place before parliament breaks for its summer recess, which begins on July 6 at the latest.
On the same day, German Finance Minister Wolfgang Schäuble insisted that Greece must stick to a March deal agreed with its international backers and enact promised reforms to remain within the eurozone.
If Greece wants to remain in the eurozone, there is no better solution than the path it has already taken," Schäuble said, referring to austerity cuts and reforms in return for a €240-billion debt bailout.
"You can't have one without the other," he added.
The Greeks need "to form a stable government and strictly respect their commitments, in the same way that we will respect our obligations to Greece," Schäuble said, echoing earlier comments by Merkel.
He spoke as Athens scrambled to put together a government after a general election Sunday failed to produce a clear winner, dealing a blow to the outgoing Pasok-New Democracy coalition that struck the bailout deal March 9 with the International Monetary Fund and European Union.
"A vast majority in Greece want at all cost to stay in the euro because the Greeks appear to have understood the advantages of a common currency, despite the constraints," Schäuble said.
"It is up to Greece to decide," he added at a conference in Brussels. "We don't need to discuss a plan B."