The government began the sale of its majority stake in FDJ on Thursday. It is expected to raise up to 1.7 billion euros from the listing, part of France's biggest wave of privatisations in more than a decade.
"It is a tremendous, popular success," Finance Minister Bruno Le Maire told BFM television, adding that retail investor subscriptions had reached 1 billion euros.
About a third of shares are earmarked for retail investors.
The bookrunner has said the IPO was oversubscribed in a range of 18.50 euros and 19.90 euros. The initial price guidance for the IPO was 16.50-19.90 euros.
Le Maire told BFM he would set a final price next week, ahead of trading that is due to begin on Nov. 21.
If the listing goes smoothly, it could embolden the government to press on with other big asset sales, such as the more lucrative but politically trickier sale of airports operator ADP and a stake in power group Engie.
The state wants to sell all or part of its 50.6% stake in ADP worth around 8.6 billion euros but opponents have organised an online referendum to stop it.
Le Maire told BFM a decision on ADP would be taken once the result of the referendum was clear, meaning it would not proceed until after local elections in March.
Regarding Engie, Le Maire said the state planned to sell the stake "at the right time" and said it would be "within months rather than before the end of the year".
(Reporting by Dominique Vidalon; Editing by Susan Fenton and Edmund Blair)