The aim of the initiative is to boost both countries' digital economies and forge closer links between cutting-edge companies from both nations.
Hancock made the announcement at an address at a landmark bilateral conference on data and the digital economy alongside his French counterpart, Mounir Mahjoubi.
He confirmed the UK's world-leading centre for AI and data, The Alan Turing Institute, is signing an agreement with the French institute, DATAIA, to promote collaboration between the French and British sectors.
The deal will see the two organisations pursue collaborative research in areas of shared interest; for example, in fairness and transparency in the design and implementation of algorithms.
They will also work together to share expertise, paving the way for visiting researchers to spend time at each Institute and hosting joint workshops and funding calls.
At the UK-France Digital Colloque - a summit of more than 350 businesses, researchers and officials from both countries - Hancock and Majoubi also signed an accord on digital government. This commits them to extending their co-operation in the digital sector on innovation, artificial intelligence, data and digital administration.
Hancock also confirmed London-based Entrepreneur First, a scheme designed to boost the UK's commitment to developing tech talent, is to continue its global expansion with a new Paris office. He also banged the drum for British tech and promoted the opportunities for business-to-business collaboration at a breakfast meeting with business leaders.
Hancock said: "The UK is a digital dynamo, increasingly recognised across the world as a place where ingenuity and innovation can flourish. We are home to four in ten of Europe's tech businesses worth more than $1bn and London is the AI capital of Europe.
"France is also doing great work in this area, and these new partnerships show the strength and depth of our respective tech industries and are the first stage in us developing a closer working relationship. This will help us better serve our citizens and provide a boost for our digital economies."