Last week, Johnson wrote to President Emmanuel Macron setting out five steps the two countries could take to deter migrants from making the perilous journey after 27 people died trying to cross the Channel.
However, France cancelled an invitation to British interior minister Priti Patel to attend a meeting on the issue after Johnson published the letter on Twitter.
Macron said he did not want to conduct diplomacy via social media and said on Friday that Britain needed to "get serious" or remain locked out of the discussions over how to curb the migrant flow.
The row deepened a rift between the two countries which are also at loggerheads over post-Brexit trading rules and fishing rights.
"It must stop. Now of course we can't just do it on our own, we do need the cooperation of the French...I hope the French will... work with us," Javid told Sky News.
He later told Times Radio: "I think the prime minister was absolutely right to set out the five areas where we certainly could cooperate more."
Patel said later on Sunday she had agreed with Dutch minister for migration Ankie Broekers-Knol in a phone call that more coordinated action was needed to tackle the crisis.
"I will continue to press this point with my European counterparts this week," she said on Twitter.
(Reporting by Elizabeth Piper, editing by Louise Heavens and Angus MacSwan)