Earlier in the day, Mr. Zelensky addressed the French parliament, saying the current conflict with Russia meant Europe was “unfortunately no longer a continent of peace”.
He also expressed hope that a summit hosted in Switzerland later this month could help bring an end to the war.
The Ukrainian president also met with French President Emmanuel Macron during his visit.
Speaking on French TV on Thursday evening, Mr Macron said Paris would send Mirage 2000 fighter jets to Ukraine and train Ukrainian pilots. He said training could begin this summer.
“You need normally between five, and six months. So by the end of the year, there will be pilots. The pilots will be trained in France,” he said.
Mr Macron also said Western allies would consider a request to send military instructors to train Ukrainian forces on the ground.
Kremlin spokesman Dmitry Peskov said the French president’s comments showed that he was willing to take a “direct” role in the Ukraine conflict.
Friday’s developments come a day after Russian President Vladimir Putin warned that Moscow could arm countries to attack Western targets.
Mr. Putin made the statement while criticizing the West’s delivery of long-range weapons to Ukraine. He did not specify which countries Moscow could supply with weapons.
Several countries including the US have given Ukraine the green light to strike targets inside Russia.
Mr Biden has permitted Ukraine to use American-supplied weapons to strike targets in Russia, but only near the Kharkiv region. The White House has said Ukraine cannot use long-range ATACMS missiles on Russian soil.