Facebook, Twitter, and other social media companies face fines for failing to remove terrorist and extremist material, under new proposals agreed by Theresa May and Emmanuel Macron.
The French and British leaders are determined to ensure the internet cannot be used as a safe haven for terrorists and criminals.
And the UK and France are jointly developing plans to create a new legal liability for companies which fail to remove unacceptable content.
Internet giants are also set to work with the respective governments to explore new ways to identify and remove harmful material automatically.
The Prime Minister is set to visit French President Mr Macron in Paris on Tuesday - just over a week on from the London Bridge terrorist attack.
Mrs May's trip to the continent also comes just days after elections in France, which appear to have been an overwhelming success for Mr Macron.
The newly elected president's party En Marche look to have secured an overwhelming dominance in parliament.
Ahead of the visit, Mrs May said: "The counter-terrorism co-operation between British and French intelligence agencies is already strong, but President Macron and I agree that more should be done to tackle the terrorist threat online.
"In the UK we are already working with social media companies to halt the spread of extremist material and poisonous propaganda that is warping young minds."
She continued: "And today I can announce that the UK and France will work together to encourage corporations to do more and abide by their social responsibility to step up their efforts to remove harmful content from their networks, including exploring the possibility of creating a new legal liability for tech companies if they fail to remove unacceptable content.
"We are united in our total condemnation of terrorism and our commitment to stamp out this evil."
Mrs May and Mr Macron will press tech companies to move forward urgently with the establishment of an industry-led forum to develop shared technical and policy solutions to the problem, as agreed by leaders of the world's most advanced economies at last month's G7 summit in Italy.
After talks at the Elysee Palace, the two leaders will watch England play France in an international football friendly.
Home Secretary Amber Rudd and French interior minister Gerard Collomb will meet in the coming days to drive the agenda forward.
Labour MP Yvette Cooper has been scathing of social media companies' "dangerous and irresponsible" approaches to extremism.
"Still today YouTube is showing illegal propaganda videos for banned jihadi and neo-Nazi extremists," she said.
"They have a disgraceful disregard for the law."