By Sudip Kar-Gupta and Gwénaëlle Barzic

Publicis said on Sunday that it would buy Epsilon from U.S. company Alliance Data, expanding Publicis' digital business and North American footprint.

Publicis shares were up 4.2 percent in early trading. Analysts at brokerage Liberum kept a "buy" rating on the stock, saying the Epsilon deal looked positive.

"With a suggested double-digit adjusted earnings per share/free cash flow accretion, the transaction looks attractive on financial terms and gives Publicis an increased amount of consumer data," the Liberum analysts said.

Publicis and other traditional advertisers, such as WPP, Omnicom and Interpublic face losing ground to new technology and software giants.

The traditional advertisers are having to cope with increasing competition from the likes of Facebook, Alphabet's Google and digital marketing specialists that track and target individual clients via their smartphones, while navigating tougher data-protection laws.

On Monday, Publicis said it expected Epsilon would boost its headline earning per share by around 12.5 percent.

"Epsilon is the ideal accelerator for Publicis' strategy," Publicis chairman and CEO Arthur Sadoun said on a conference call.

(Reporting by Gwenaelle Barzic and Sudip Kar-Gupta. Editing by Jane Merriman)

By Sudip Kar-Gupta and Gwénaëlle Barzic