He said discussions could take place “very quickly” if the British are prepared to enter negotiations in a “serious spirit”.
A Government source said it appeared to be a “positive” move after the diplomatic row which erupted following the capsize last week of a migrant boat with the loss of 27 lives.
Mr Johnson infuriated French president Emmanuel Macron when he posted a letter on Twitter calling for joint patrols on French beaches and the return to France of migrants who succeed in making the dangerous Channel crossing.
Mr Macron said it was not a serious way to negotiate, while Home Secretary Priti Patel was disinvited from a meeting in Calais on Sunday of ministers from France, Belgium, the Netherlands and Germany to discuss the crisis.
But speaking at a press conference on Monday, Mr Darmanin said the two countries needed to work together to deal with a shared problem.
“From the moment there is no more double-speak, and we can discuss in a serious spirit, and our private exchanges correspond to our public exchanges, the French government is ready to very quickly resume discussions with Great Britain,” he said.
Mr Darmanin said said the proposals by Mr Castex could include ways to open up legal routes to the UK and for asylum seekers and to allow unaccompanied minors to join relatives in Britain.
However he said France could not accept the practice of turning back boats at sea, adding “This is a red line for the French government”.
Meanwhile Mr Johnson is due to hold talks online with another of the key European players – Belgian prime minister Alexander de Croo.
Downing Street continues to insisted a returns agreement, as set out by Mr Johnson in his letter, would be the “single biggest deterrent” to migrants attempting the Channel crossing.