"Victory for Freedom! As I have been asking for years we must now have the same referendum in France and EU countries," the National Front (FN) leader tweeted.
The eurosceptic, anti-immigration FN has accused the EU of suffering a "democratic deficit" and has long urged all members of the bloc to follow Britain's example.
The Brexit vote is likely to fire up eurosceptic populists across the bloc, with Dutch far-right MP Geert Wilders also calling for an EU referendum in his own country following the result.
Fears are high that a domino effect could see other countries following in Britain's footsteps, threatening the core of the European project.
"France has possibly a thousand more reasons to want to leave the EU than the English," Le Pen said at a gathering of far-right parties in Vienna last Friday.
Le Pen has accused the EU of pursuing closer integration "against our will".
She says the Union is responsible for high eurozone unemployment and has failed to keep out "smugglers, terrorists (and) economic migrants."