"We're at a turning point in Europe that requires mutual confidence", he said.
Mr Macron added, however, that "what I know is that we have investments to make (in Europe), and so we have to work on investment mechanisms for the future".
The draft is expected to be approved by the SPD's party leadership next week and is likely to be adopted at a party congress on June 25.
During Macron's first foreign visit since his inauguration Sunday, he told Merkel that he was "happy" to work together with Germany "on a common roadmap for the European Union and the eurozone".
And, despite the smiles on Monday, Mr Macron has yet to prove himself.
Macron is the conservative Merkel's fourth French president in almost 12 years as chancellor.
Underlining concerns over Macron's proposals, Germany's biggest selling daily Bild warned that before seeking deeper European Union integration, "France must once again be at the same level as Germany politically and economically".
The most senior Cabinet job, interior minister, went to Gerard Collomb, 69, long-time Socialist mayor of Lyon who played a key role in Macron's presidential bid.
"Our relationship needs more trust and more results", said Macron, adding that relations between Merkel and his predecessor Francois Hollande, were not especially close or productive.
At home, Macron started to shape his government by appointing relatively little-known lawmaker Edouard Philippe, 46, as his prime minister.
After his meeting with Merkel, Macron stressed that he was not in favour of eurobonds - loans underwritten by all members of the eurozone, which some conservative German politicians have described as a vision of "hell" for their voters.
Mr. Macron also called on the European Union to toughen its policies against countries that flout the rules of worldwide trade. The German media initially embraced Macron's victory, with headlines like "France says yes to Europe", "Macron wins it for Europe", and "No Frexit" greeting readers the morning after the election victory.
Ms. Merkel and her government have always been skeptical of proposals to pool more resources, believing that sharing eurozone money could let countries off the hook when it comes to balancing their budgets and making necessary reforms.
Mr Macron sought to bat away German fears on debt, saying he was opposed to mutualising "old debt" between euro-zone countries.
Macron, who trounced far-right anti-EU leader Marine Le Pen in the election, urged a "historic reconstruction" of Europe to battle the populism sweeping the continent and widespread disillusionment with the bloc. "We need more pragmatism, less bureaucracy and a Europe that protects our citizens".
The statement was a clear nod to Germany, which has been vigorously opposing the idea of taking responsibility for the debts of weaker, crisis-hit European Union member states.
He intends to press for the creation of a parliament and budget for the eurozone which would see Germany, the zone's richest member, contribute funds to support economic growth in weaker nations.