The tax, known as the FTT, has seen finance heads from eleven European countries at loggerheads for the past three years.
Following the global financial crisis, the European Commission had argued in favour of a tax on stocks, bonds and derivatives, claiming that it could raise up to €57 billion a year for the EU if it was implemented across all 28 member states.
But discussions over an EU-wide implementation of the measure have stalled as countries are unable to agree on which transactions would be taxed, as well as the level of taxation.
On Thursday, the French Finance Minister Michel Sapin and his Austrian counterpart Hans-Joerg Schelling penned a letter attempting to introduce a compromise idea. The two countries suggested that the taxes should be applied at a lower rate than previously proposed, but across a wider range of services.
"The very tax base has gradually been stripped of meaning, particularly in the case of derivatives," they wrote.
"We suggest resuming the work on a different footing to the approach that led to negotiations hitting a wall in 2014. This fresh direction would be based on the assumption that the tax should have the widest possible base and low rates."
The move has been strongly opposed by the UK, where officials fear the tax would push business away from London. Sweden is also concerned that the tax may impact local and European business, citing that the Swedes faced economic problems after introducing their own FTT during the 1980s.
Both countries - which are not in the eurozone - have also criticized the "secretive" way that countries using the single currency have conducted talks on various FTT proposals.
Finance expert Tomasz Michalski, from HEC business school in Paris, told The Local on Friday he doubts the plan will ever win enough support.
"I think they are just prancing around. Austria is too small a player and it looks like the French government is just suggesting this to try to win support on the left," Michalski said.
"After their recent rise in popularity, perhaps they want to return to some of the promises they made before Hollande was elected in 2012, when he declared the world of finance as his enemy.
"There's not enough support among northern European countries for this. The UK is against it and Germany is reluctant because of the impact on its financial centre in Frankfurt."