The issue has become a major source of contention within Brexit negotiations.
London has committed to avoid a “hard border” with checkpoints between Northern Ireland, part of the UK, and EU-member Ireland, which all sides agree is vital to maintaining the 1998 Good Friday peace accords.
But Britain has also said it will not enter into a customs union with the EU post-Brexit and has been urged to find a solution to reconcile the two positions.
The EU has suggested a “backstop” proposal, in which only Northern Ireland would stay in a customs union with the EU post-Brexit.
French foreign minister Jean-Yves le Drian said all sides should set themselves a clear deadline of next month to come to a decision.
“What we want is for things to go quickly and a June deadline chosen as the final deadline otherwise the withdrawal agreement will be more complicated,” he told reporters in Dublin before a meeting with his Irish counterpart Simon Coveney.
Britain is due to leave the European Union in March 2019 and Brussels wants negotiations completed by October.
Britain wants to be free of the EU customs union in order to be able to strike trade deals with the rest of the world post-Brexit.
But British Prime Minister Theresa May faces stiff opposition from within her own party which is bitterly divided on what sort of customs agreement the UK should have.
On Sunday she penned a column in The Sunday Times newspaper saying she had proposed different options for a new customs arrangement with the EU and that the government would continue to work on them during the negotiations.
She said any deal must protect the United Kingdom's constitutional and economic integrity and honour the Northern Irish peace accords.
“This means there can be no hard border between Northern Ireland and Ireland, or between Northern Ireland and the rest of the UK,” May wrote.
“Any agreements must create as little friction as possible for trade,” she said, adding: “We must not constrain our ability to negotiate trade agreements with other countries around the world by being bound into a customs union.”