Emmanuel Macron has promised "concrete, effective and lasting" co-operation on migration as Sir Keir Starmer comes under increasing pressure to stop illegal Channel crossings.
The French President and Prime Minster will lead a Franco-British summit later in the week with action on people trafficking gangs and small boats set to be top of the agenda.
In the last seven days more than 2,000 migrants have made the perilous journey across the water from France, Home Office figures show.
"Together, we will address the major challenges of our time: security, defence, nuclear energy, space, innovation, artificial intelligence, migration and culture,” Mr Macron said.
"These are all areas in which we seek to act together and deepen our co-operation in a concrete, effective, and lasting way."
Britain hopes plans could include a "one in, one out" deal to exchange Channel migrants for asylum seekers in Europe who have a British link.
Such an agreement is believed to still to be on the table, but a deal has not yet been done. Ministers have also been pushing for France to revise its rules to allow police to intervene when boats are in shallow water, rather than requiring them still to be on land.
Last week, French authorities appeared to change tactics when officers used a knife to puncture an inflatable boat after it had launched.
But Downing Street has suggested a new approach had been discussed but not yet rolled out.
A spokesman for Number 10 said: “We are the first Government to have secured agreement from the French to review their maritime tactics so their border enforcement teams can intervene in shallow waters.
“This is operationally and legally complex, but we’re working closely with the French. We expect this to be operationalised soon.”
Mr Macron will be hosted by the King during his three-day state visit, the first by a French president since 2008.
On Tuesday morning the Prince and Princess of Wales travelled to RAF Northolt in west London to welcome the Macrons on behalf of the King .
His state visit comes a week after the total number of people crossing the Channel in small boats this year passed 20,000.
The total now stands at 21,117 and is a record for this point in the year.
During Mr Macron’s visit, he is expected to address Parliament, as his predecessor-but-one, Nicolas Sarkozy, did during his state visit in 2008.
Sir Keir and the French president are also expected to co-host a meeting of the “coalition of the willing”, the peacekeeping mission proposed to be deployed to Ukraine in the event of a ceasefire with Russia.
The Prime Minister spoke to Ukrainian President Volodymyr Zelensky on Monday afternoon ahead of the talks, agreeing to provide an update on the “significant progress” being made by coalition planners.
Meanwhile, Liberal Democrat leader Sir Ed Davey urged Sir Keir to use the state visit to create a “united front” against Donald Trump’s “damaging trade war”.
