The meeting at the Elysee Palace, which took place as US President Donald Trump was in Paris as the guest of honour for Bastille Day events, underscores Macron's wish "to build ambitious and concrete projects," the French leader told regional daily Ouest-France.
Macron was elected in May promising to overhaul the 28-member bloc with a host of initiatives to deepen EU integration in the areas of defence, security and immigration.
The 39-year-old French leader is keen to revive the traditional "engine" behind European integration -- the post-war alliance of Paris and Berlin which ended centuries of conflict.
But with less than three months before Germany's legislative elections, it will be difficult for Paris and Berlin to move ahead on key issues such as the reform of the eurozone.
The French leader has proposed creating a finance minister, parliament and budget for the eurozone, which would require changes to EU treaties.
"I want the eurozone to have more coherence and convergence," Macron said in the Ouest-France interview.
'The fate it deserves'
Macron warned Germany that it must move to correct the "dysfunctions" of the eurozone and give it "the fate it deserves".
"France must reform its economy to give it more vigour," he added, but Germany, for its part, "must support a revival of public and private investment in Europe".
Merkel has agreed to consider the issues, but they will have to wait until after the elections, which her centre-right Christian Democratic Union (CDU) is expected to win.
The French leader is also set to press Merkel for a financial and military contribution to a joint anti-jihadist regional force called the G5 Sahel made up of forces from Burkina Faso, Chad, Mali, Mauritania and Niger.
It is not the first time the French and German governments have held a joint cabinet meeting -- the last one was in April -- but both sides are keen to capitalise on the momentum generated by Macron's victory in May.
The bloc is still grappling with the fallout from Britain's shock vote to exit the EU in a referendum in June 2016.
But Brexit, along with perceived threats from the United States under president Donald Trump, as well as from Russia, has given it a renewed sense of purpose.
Merkel and Macron were to meet later with their defence and security chiefs in talks expected to focus on joint defence and counter-terrorism issues, followed by a joint news conference at 1200 GMT.
The EU last month created a European defence fund with an annual budget of 5.5 billion euro, laying the basis for permanent military cooperation.
Macron will host Trump for talks in the afternoon, before they head to dinner at a Michelin-starred restaurant in the Eiffel Tower.