President Emmanuel Macron needs a clear majority in parliament to be able to pass laws and endorse his prime minister, Edouard Philippe.
Israeli Prime Minister Benjamin Netanyahu has openly expressed his support for Habib, making a video in May in which he praised the French lawmaker in French and Hebrew.
The survival of the Socialist Party, which ruled France for the past five years but is forecast to get just 15 to 30 seats, is at stake, as is the unity of The Republicans. The lower house is called the National Assembly, and the upper is the Senate.
The former banker and economics minister who had never before held elected office gambled correctly that voters were ready for something completely new: a movement occupying the political centre ground, made up largely of new faces, many of them with no political experience at all.
As when voters turned the previously unelected Macron into France's youngest president last month, Sunday's first round of voting in two-stage legislative elections again brought stinging black eyes to traditional parties that, having monopolized power for decades, are being utterly routed by Macron's political revolution.
A total of 7,882 candidates are standing nationwide in a process expected to produce a thorough overhaul of the National Assembly as more than 200 of the outgoing MPs are not seeking re-election.
But turnout was at a record low level, and that could cloud Macron's mandate.
Runner-up in France's presidential election, Ms Le Pen urged "patriotic" voters to turn out en masse in the second round on June 18 and boost her party's small presence in the National Assembly.
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There are also concerns that Sessions might have helped subvert the ongoing Russia-related investigations. He said during his confirmation hearing that he had not met with Russians during the campaign.
Macron has enjoyed a smooth start in the five weeks since he beat far-right candidate Marine Le Pen to become France's youngest-ever president, naming a cabinet that crosses left-right lines and making a big impression at global summits. French voters are choosing lawmakers in the lower house of parliamen.
Voters in Guiana, Guadeloupe, Martinique and other overseas French territories headed to the polls on Saturday to cast their ballots in the parliamentary elections.
Meanwhile, the Socialist Party, according to projections, was expected to take less than 40 seats, while the far-right National Front led by Marine Le Pen and left-wing France Unbowed looked toward an uncertain outcome.
If no candidate wins more than 50 percent in the first round, all candidates who secure at least 12.5 percent will go into the second round.
The National Front and Jean-Luc Mélenchon's far-left party will also hope to take advantage of the disillusionment with the establishment.
Voter rejection of old-style, established politics - already seen in the April-May two-round presidential vote that handed power to 39-year-old Macron - was again manifest in the legislative vote. That compared to 48 percent at the same time in the first round five years ago and 49 percent in 2002.
The second phase of elections will be held next Sunday to determine the course of French Government and politics.
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