After talks with British Prime Minister Theresa May in Paris, French President Emmanuel Macron said both countries agreed that social networks were not doing enough to stamp out terror propaganda.
Speaking after terror attacks in Manchester and London, Macron said the two countries had worked on a "very concrete" action plan.
He said one of the key measures would aim at preventing the incitement of "hate and terrorism" on the internet.
May said she and Macron agreed that "more should be done to tackle the terrorist threat online".
She said the British and French campaign was aimed to "ensure the internet cannot... be used to host the radicalising material that leads to so much harm."
May said the British government was already working with social media companies "to halt the spread of extremist material and poisonous propaganda that warps young minds", adding: "But we know they need to do more.
"Today we can announce that the UK and France will work together to encourage organisations to do more and abide by their social responsibility to step up their efforts to remove harmful content from their networks."
The campaign includes exploring the possibility of legal penalties against tech companies if they fail to take the necessary action to remove unacceptable content, May said.
Britain was rocked by a suicide bombing at a pop concert in Manchester on May 22 which killed 22 people, including children, followed two weeks later by a knife and van attack in central London, which left eight dead.
France has been a constant target for jihadist attacks since 2015, with more than 230 people killed.
After their press conference the two leaders headed to the Stade de France to watch a friendly match between the French and English.