Both Marine Le Pen and Jean-Luc Melenchon are Eurosceptic
The EU said it does not have a plan for the doomsday scenario and an official has revealed such a decider could kill the bloc.
This, the unnamed official said, could have such a devastating effect on Brussels that it may "cease to exist".
If Marine Le Pen wins the election, the European Union as we know it ceases to exist
Even without a shock outcome, Brussels worries that neither of the more mainstream candidates, including centrist Emmanuel Macron and centre-right Francois Fillon, can revive France's economy or help confront doubts about the EU's future.
One senior European Union diplomat said: "If Marine Le Pen wins the election, the European Union as we know it ceases to exist.
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"Then we have to think about other models… There is no Plan B. The city is shivering inside."
A senior Eurozone official also said Marine Le Pen as president would be devastating for the bloc – even if the Front National leader failed to actually pull France from the union.
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Klaus Regling, managing director of the eurozone's bailout fund, told a forum in Washington this week he doubted Le Pen would gain support to pull off a Frexit.
But he warned: "It would mean a standstill, growth would remain low."
EU leaders will be able to take stock of any first round surprise at a summit on April 29 arranged to discuss preparations for Britain's exit negotiations.
In a vote too close to call, some EU diplomats see Mr Macron as the best bet to defeat Le Pen in the second round and heal rifts inside the EU.
As a former economy minister under outgoing president Francois Hollande, he won fans among France's EU partners through his enthusiasm for pro-business reforms.
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Jean-Luc Melenchon addresses supporters from a boat
With Brexit pending, Brussels needs a strong France to reinvigorate the EU and make the euro zone stronger and more sustainable.
German chancellor Angela Merkel has received both Macron and Fillon in Berlin but not, notably, Ms Le Pen or Mr Melenchon.
An EU official has warned the bloc could 'cease to exist' under a Le Pen presidency
Political analyst Lafont Rapnouil said: "The fact that Le Pen and Melenchon didn't go to Berlin speaks volume about the difficulties which would arise if either was elected.
"Macron's unabashed pro-integration positions, his orthodox economic ideas and his insistence on the key relation with Berlin make him – on paper – a likely Berlin favourite."