The indicative price range for the French public offering and the international offering is 14.20-17.40 euros per share, with pricing expected on June 15.

SocGen has said that the share sale, France's biggest IPO in more than 18 months, will help to accelerate development of ALD, which manages a worldwide fleet of 1.4 million vehicles.

The initial sale of 80,820,728 existing shares, representing 20 percent of ALD's share capital, will bring gross proceeds between 1.148 billion euros and 1.406 billion euros, the bank said in a statement.

Assuming the exercise in full of the overallotment option, the total size of the global offering will range between about 1.32 billion euros and 1.62 billion euros, the statement said.

This would value ALD at between 5.74 billion euros and 7.04 billion euros.

ALD shares are expected to start trading on Euronext Paris on June 16, SocGen said, adding that it would remain ALD's controlling shareholder.

The biggest IPO on the Paris Euronext exchange since asset manager Amundi's offering in November 2015 is expected to boost SocGen's capital ratio by up to 20 basis points.

"As an indication, a disposal of 23 percent of ALD's share capital would have a positive impact between 12 basis points and 20 basis points on the CET1 ratio," it said.

Credit Suisse, JP Morgan and SocGen are joint global Coordinators on the IPO, with BofA Merrill Lynch, Barclays, Citigroup, Deutsche Bank and HSBC acting as joint bookrunners.

(Reporting by Ingrid Melander and Dominique Rodriguez; Editing by David Goodman)