PARIS - President Francois Hollande's Socialist Party and allied leftist groups appeared headed for a working majority in parliament after the first round of France's legislative elections Sunday. Exit polls showed that the Socialists and their allies were likely to win easily more than half of the 577 seats in the National Assembly, the lower house of parliament, if the results are confirmed in a runoff round scheduled next Sunday. Hollande's Socialists already control the Senate, giving Hollande the prospect of a free legislative field for his program designed to lighten the burden imposed by Europe's financial crisis on lower-income French families. Among measures promised by Hollande during his election campaign were tax increases for the rich, a hike in the minimum wage and earlier retirement for those who have worked more than 40 years. Hollande, who took power after defeating Nicolas Sarkozy just over a month ago, has had Prime Minister Jean-Marc Aryrault implement some of the measures by decree in what was denounced by conservatives as an electioneering stunt and praised by leftists as a swift fulfillment of campaign promises. Analysts cautioned that the match-ups in next Sunday's voting could produce unexpected results based on the personalities of candidates and other local factors in widely varying districts spread across this nation of 65 million people. Citing this possibility, Jean-Francois Cope, secretary general of the conservative Union for a Popular Movement, called on rightist voters to continue the struggle in another burst of campaigning this week. "The game is not that over yet," he said. Hollande's foreign minister, Laurent Fabius, said the first round shows that voters wanted to be coherent with their presidential vote on May 6 . But he also pointed out that the opening for a Socialist legislative majority has to be confirmed in the runoff round, and urged Hollande's followers not to be complacent. The exit polls, approximations taken for several television stations, gave the Socialists between 270 and 335 seats to the Conservatives" 235 to 270. The Greens Party, which has an electoral alliance with the Socialists, was estimated to have won between 12 and 18 seats, and the Leftist Front, a far-left group headed by Jean-Luc Melenchon, was headed for a win of more than a dozen. The outcome, assuming it is confirmed next Sunday, means the Socialists probably will have to rely on support from the Greens and the Melenchon group to pass some legislation. Conservative commentators have warned this could force Hollande to take a more leftward course than he would be inclined to adopt. "The Socialists should rethink their alliance with the Leftist Front," former prime minister Francois Fillon said after the results became known. Fabius predicted, however, that the Socialists and the Greens would be able to form a majority without help from the Leftist Front. Melenchon was eliminated after a bitterly fought first-round campaign against Marine Le Pen of the far-right National Front in the northern France city of Henin-Beaumont.