The two leaders, both ardent pro-Europeans, declared their "determination to further deepen cooperation" between their countries in the statement.
And, in a video recorded during Merkel's visit to Paris on Friday and posted on social media, they appealed to young people to build friendship between their peoples.
On Monday French MPs will travel to the German parliament and German MPs will visit the French one to discuss drawing up a new Franco-German treaty.
EU motor force
The Elysée Treaty, signed by Charles de Gaulle and Konrad Adenauer on 22 January 1963, was designed to end war between the two countries.
Since then they have been the motor force in the EU, a role that Merkel and Macron believe is even more important with the crises that have hit the bloc over the last year.
Their statement said that a new treaty would increase economic integration and harmonise legislation.
They also called for "ambitious measures to promote reciprocal teaching of [our] languages".
Despite Sunday's vote by Germany's Social Democrats to join a coalition with Merkel's Christian Democrats, the long-drawn-out negotiations weakened her position in the partnership, strenghening Macron's drive for EU reforms, including a common budget for the bloc.