The government is selling 52 percent of the state lottery monopoly, Francaise des Jeux (FDJ), in order to raise money for investment in innovation.
It has launched a huge marketing drive to try attract as many individual French investors as possible.
Since the sale began on November 7, "there has been 1 billion euros in subscriptions from individual shareholders," Le Maire told France's BFM news channel, calling it "an immense success for the people."
Individual shareholders, for whom a third of the shares have been reserved, have until November 19 to subscribe.
Institutional investors have until November 20, a day before FDJ is floated on the Paris stock market.
Le Maire said that small-time investors, who are being offered a two-percent discount, would be given priority if the shares were over-subscribed.
The government hopes the sale will rekindle demand for stocks among French savers, many of whom have stuck with ultra-safe low-interest savings accounts since the 2007-2008 financial crisis.
The shares have an indicative price of 16.50-19.90 euros, which would value FDJ at up to 3.8 billion euros.
FDJ is the successor of a national lottery founded in 1933 to help soldiers disfigured in World War I and struggling farmers.
It is the second-biggest betting company in Europe and the fourth in the world.
The state will retain a 20 percent stake in the company.
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