"The further investment we have agreed today will make the UK's borders even more secure," May said during a joint press conference with Macron.
In addition to more funds from Britain, the two sides agreed to "improved treatment" of unaccompanied child refugees which Macron said would see their paperwork processed within 25 days.
May also committed to sending Royal Air Force helicopters to France's military operation in Mali.
Bayeux tapestry loan in doubt
She also confirmed that France will lend Britain the Bayeux Tapestry, a historic work depicting the Norman conquest of England which she said would come to Britain in 2022, for the first time in over 900 years.
"We are somehow making a new tapestry together," Macron said.
But French experts said the artefact cannot be sent abroad until major conservation problems are resolved.
Curator Pierre Bouet, who cares for the tapestry at the museum in the Normandy town from which it takes its name, said he thought "it was a hoax" when he first heard of the plan.
"If you were to ask my advice, despite the regard I have for my English colleagues who I have worked with for many years, I would say no," he told the AFP news agency.
Moving such a "fragile, near-1,000-year-old roll of wool and linen" even a few metres was risky, never mind transporting it overseas, the museum' s former director Isabelle Attard said.
"A temporary exhibition in Britain is worrying on several levels," she said, adding that she had "huge doubts" about whether such a loan was practically possible.