MEPs approved an overall package of reforms including a system giving the largest group in parliament the right to choose a successor to European Commission chief Jean-Claude Juncker.
But they voted against a plan for so-called "transnational lists" - which would allow 30 of the 73 seats vacated by Britain to be elected on pan-European tickets, instead of by standing in individual member states.
Macron, the energetic young French leader, had strongly backed the idea as part of his ambition for a sweeping reboot of the European Union once Britain leaves in March 2019.
Macron's office said it regretted the European Parliament's decision but said that "France will continue to defend this idea" in the future.
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He won support from Luxembourg's Prime Minister Xavier Bettel, who questioned why national leaders would now back the system for picking a new EU commission chief - called Spitzenkandidat, or leading candidate in German.
"Why should we have Spitzenkandidaten if we have no transnational list for elections?!" he said in a personally signed tweet.
Varoufakis, the leftist who led a brief but fiery resistance against the eurozone in bailout talks in 2015, said today's decision was a "major own goal, but weep not!", as he was coordinating a list of candidates in several countries to join forces.
The next European elections will take place in May 2019, two months after Britain leaves the EU.
The European Parliament warned today that it would vote against any candidate to replace Juncker who was not chosen by the assembly's biggest political bloc.
The system - widely known as "Spitzenkandidat" or lead candidate - was used to pick Juncker in 2014 and MEPs say it makes the choice more democratic.
But it is opposed by many national leaders who view it as a backroom stitch-up that freezes out the governments of EU member states.
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