This protest against politics-as-usual is what catapulted Macron, a former government official who has never held elected office, into the Elysee Palace. He doesn’t belong to a party and only founded his “On the Move” movement a year ago. But the political independence that proved an asset during the presidential campaign could become a liability during parliamentary elections in June.

Macron has promised to field On the Move candidates in every French electoral district, and polls suggest the movement could win more seats in France’s National Assembly than any other party—maybe even enough to achieve a majority in the 577-seat lower house, which would be astonishing for an organization that has only just burst onto the political scene.

If, however, Macron falls short of a majority, he will need to form a governing coalition with other parties. And if another party wins a majority, he will need to deal with that rival party, in a scenario the French refer to rather euphemistically as “cohabitation.”

In France, presidents have for the last several decades generally been drawn from the major center-left or center-right party. Their victory in presidential elections has typically paved the way for their party to win a majority in parliament, allowing the president to appoint a prime minister from his party who will run the government according to the president’s wishes. This hasn’t always occurred; the Fifth Republic has experienced cohabitation three times. But the system has been running smoothly for a while: France hasn’t endured divided government since a constitutional amendment in the early 2000s that made both presidential and parliamentary terms five years, and scheduled parliamentary elections shortly after presidential elections to reduce the likelihood of cohabitation.

“During cohabitation periods, the presidency diminished in stature, and the premier tended to exercise the main executive policymaking authority,” writes John Carey, a comparative-politics professor at Dartmouth College. “For example, in the late 1980s, [Jacques] Chirac as premier engineered a major tax cut and privatized state-owned enterprises while the Socialist [President Francois] Mitterand could only watch. But when Chirac was president, Socialist Party Premier [Lionel] Jospin pushed through legislation to shorten the workweek from 39 hours to 35.”

Now, however, France’s traditional party system has imploded—and the risks of cohabitation and political dysfunction have returned. If an opposition party ends up controlling the National Assembly, Macron will likely be blocked from carrying out his ambitious policy agenda, which includes cutting government spending and giving employers more flexibility to hire, fire, and negotiate with employees. If he has to cobble together a coalition of diverse factions, he will have to painstakingly build support for each vote on each piece of legislation. As Francois Fillon, the Republican candidate who lost in the first round of the presidential election, memorably put it, Macron might have to again and again “cook up parliamentary dishes of impotence and compromises”—the very worst kind of French cuisine.