Sapin said the resolution, to be debated Thursday, would send a "very strong political message: the fight against the financing of terrorism is one of the priorities of the United Nations' members and every state must take the necessary measures."
And ahead of Thursday's meeting with of all 15 finance ministers of Security Council member states -- the first of its kind -- Sapin warned that countries that fail to turn off the tap on jihadists' funding could potentially face sanctions.
France requested the meeting following the terror attacks in Paris last month that left 130 people dead and were claimed by IS.
Sapin has made cutting off extremists' financing a key goal since the French capital was first hit by jihadists in January, when gunmen attacked the Charlie Hebdo magazine and a Jewish supermarket.
Based on an earlier resolution targeting Al-Qaeda, the new text "will be explicitly extended to Daesh", Sapin said, using another term for IS.
He added that it will "in particular aim for the freezing of assets that in one way or another stem from oil smuggling".
"It will also demand that states exercise special vigilance with regard to the smuggling of works of art that could feed big movements like Daesh," the minister said.
- International pressure -
Adam Szubin, the US Treasury's acting undersecretary for terrorism and financial crimes, said last week that IS has reaped more than $500 million (460 million euros) in black market oil sales, looted bank vaults captured in Iraq and Syria, and raised millions more through extortion.
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But to run what amounts to a mini-state, it needs steady and renewable sources of funding -- so it needs access to the international financial system to move money and import supplies, according to Szubin.
Sapin said he expects the UN resolution to be passed unanimously.
"I cannot see what country could oppose effective action in the fight against the financing of terrorism," he said.
The UN resolution would provide "legal support" to countries taking action against IS finances, Sapin said.
The international community would then need to ensure that states were taking the same measures -- a task that would fall to the Financial Action Task Force (FATF), a Paris-based intergovernmental body that develops policies against money laundering and terrorist financing.
"Each country would be subject to review to see if it has taken all the necessary measures," Sapin told AFP.
In this way, international pressure would play a key role in ensuring that countries do the most possible to cut off jihadists' cash -- or risk potential sanctions themselves.
"No country can appear soft on the financing of terror, or they could be placed on a list," he said.
"From that moment, sanctions could be taken against the country."
Sapin will meet separately with US Treasury Secretary Jacob Lew -- who is chairing the finance ministers' meeting as Washington takes on the rotating Security Council presidency this month -- to discuss information-sharing on terror financing.
"We must improve, speed up and deepen these exchanges of information, especially from a network that the Americans have the ability to analyse -- the SWIFT system -- that takes in the movement of funds across the planet," Sapin said.