Speaking in Downing Street, the centrist politician called his own country "a very attractive space".
Mr Macron called for a "fair execution" of Brexit.
The French government has been wooing London-based financial companies, but the UK government has promised to fight to maintain the City's position.
HSBC said last month that it was preparing to move 1,000 jobs to Paris.
Speaking after talks with Mrs May, Mr Macron was keen to emphasise his enthusiasm for such developments, telling reporters: "I was very happy to see that some academics and researchers in the UK, because of the Brexit, would consider to come to France precisely to work."
Asked if he wanted banks to move to Paris after Brexit, he said: "I want banks, talents, researchers, academics and so on.
"I think that France and the EU are a very attractive space."
Mr Macron, who appeared alone in Downing Street after his meeting, said there was a "series of initiatives" aimed at getting "talented peopleâ€¦ working here to come to France".
The former economy minister and investment banker added that despite the UK leaving the EU, there should be "further co-operation in terms of defence" between it and France.
On the future of French nationals in the UK, Mr Macron said: "I will be very careful about the way for our people to be allowed to stay here and work in good conditions."
Last week, Mrs May stressed the importance of an early deal to establish the rights of EU citizens living in the UK and UK citizens living in other EU countries.
Mr Macron has largely been in third place in recent French presidential opinion polls, behind the National Front's Marine Le Pen and Republican Francois Fillon.
In some, he has come second.
Further polling suggests that, if he came second overall to Ms Le Pen in the first round of voting and entered a final run-off against her, he would win the presidency.
After speaking to the media, Mr Macron walked around Westminster, stopping to chat and appear in selfies.
A Downing Street spokesman said Mrs May and Mr Macron had had "a private conversation".
Asked whether the French politician had been invited, he said: "He is in London, and we have been able to accommodate him."
French presidential candidate Emmanuel Macron has said he would like UK banks and workers to relocate to his country, following discussions with Theresa May.