Britain had previously agreed to take in a total of 480 unaccompanied minors from France, and had taken in 220 of them, but then imposed new admission criteria.
"We have agreed to amend the eligibility date on an exceptional basis to ensure we can transfer the circa 260 remaining unaccompanied children," Home Secretary Amber Rudd said in a statement.
Opposition Labour politician Alf Dubs, who had pushed Britain into taking in unaccompanied young migrants, had proposed that Britain take in 3,000 children.
Britain had earlier set a cut-off date, saying it would only accept unaccompanied minors who had arrived in Europe before March 20, 2016. It said that date had now been extended to January 18, 2018.
"The government has not agreed to any new obligations to take more unaccompanied children from Europe," Rudd said, adding that the agreement with France "will help ensure migrant camps do not re-form".
Britain and France will "jointly work upstream in source and transit countries to discourage migrants who do not have any lawful basis for doing so from making the dangerous journey to northern France," she said.
May hosted Macron for a summit on Thursday where the two agreed on a new border treaty under which Britain will pay an extra £44.5 (€50 million, $62 million) to fund tighter security in Calais.