The UN Security Council is expected to vote Thursday on a resolution to haul Syria before the International Criminal Court, although Russian and Chinese opposition will likely doom the measure.
If China and Russia exercise their veto power, it would be the fourth time they do so on Western resolutions since the start of the Syrian crisis three years ago.
The text drafted by France aims "to send a message that there is accountability for the crimes committed in Syria," a diplomat said.
"There is a clear need to demonstrate that the international community is interested in accountability."
Next week's Security Council vote comes amid growing suspicions that Syria has been using chemical weapons on its own people.
"It's not because there is a risk of veto that we should encourage impunity for (Syrian President) Bashar" al-Assad, French Foreign Minister Laurent Fabius said Thursday during a meeting in London of the Friends of Syria group, which backed the French proposal.