Valls was the victim of a subtle trolling from the official Twitter account of the show after his government moved on Tuesday to bypass the country's parliament to force through a wildly unpopular labour reform law that has brought hundreds of thousands of protesters to the streets.
If the author's meaning was in doubt, they helpfully added the hashtag "LoiTravail", or labour law, and illustrated their tweet with an animated GIF of Underwood's character chuckling mirthfully.
They even included the hashtag "49al3", a reference to the law with which Valls hopes to bypass parliament -- article 49.3 of France's constitution.
But not to be outdone, Valls shot back an hour later with words of wisdom belonging to World War II British prime minister Winston Churchill.
"Dear Frank," wrote Valls, addressing the fictional president Underwood.
"Democracy is the worst form of government except for all others Never forget!" he wrote, punctuating his tweet with a winking emoticon and illustrating his social media salvo with a black and white picture of Churchill flashing a victory sign.
The labour reforms, which would make it easier for employers to hire and fire workers, is viewed as the last major piece of legislation for President Francois Hollande as the clock ticks down on his term in office.
But Hollande, one of the least popular leaders in modern French history, has faced fierce and vocal opposition from within the ranks of his own party, making passage through parliament unlikely.
Hollande has previously resorted to article 49.3 of the constitution to force through another controversial reform, this time governing trading hours and the deregulation of some sectors.
When he was in the opposition, however, he had criticised former president Nicolas Sarkozy for resorting to the same tactic.
In "House of Cards", the character of president Underwood is legendary for his constitutional manoeuvrings, using legal loopholes and political bargaining to advance his own power.