"We will... take further steps toward a political union in Europe, and we invite the other European states to join us in this endeavour," Frank-Walter Steinmeier and Jean-Marc Ayrault wrote in a joint position paper.
The top diplomats of the two core EU founding members and biggest economies said that "Germany and France have a responsibility to strengthen solidarity and cohesion within the European Union".
But they also signalled a willingness to accept a multi-speed union, writing that "we must... acknowledge that there are different degrees of ambition towards further integration among the member states".
The two centre-left politicians proposed closer cooperation in three key policy areas - internal and external security, the migrant and refugee crisis, and on fiscal and economic cooperation.
A spokesman for German Chancellor Angela Merkel, a conservative, said that she had read the paper and considered it one of the many contributions that would shape the way ahead for the EU, as its government leaders agree on a common policy.
Ayrault and Steinmeier wrote in the paper, published in both German and French, that after the Brexit vote last Thursday, "the right answer is neither a simple call for 'more Europe' nor a mere phase of reflection".
But they stressed that "Germany and France remain firmly convinced that the European Union is a historically unique and indispensable framework for the pursuit of freedom, prosperity and security in Europe, for fostering peaceful relations between its peoples and for helping bring peace and stability in the world".
"Our two countries share a common destiny and a common set of values. Both together are the foundation for an ever closer union of our peoples."