Gemalto's shares were up about 33 percent by 1229 GMT to 45 euros ($52.96), just one euro below the price Atos has offered in its takeover proposal made late on Monday.

Atos shares were up more than 6 percent and were the biggest gainer in France's CAC 40 index.

Gemalto said in a statement its board would reply to Atos' unsolicited bid by Friday.

The all-cash bid comes after a difficult period for digital security company Gemalto, which in July made its fourth profit warning since October 2016.

The bid also comes against a backdrop of higher spending on cyber security worldwide, with research firm Gartner forecasting that 60 percent of organisations will invest in multiple data security tools up from 35 percent currently.

"After a terrible year 2017, Gemalto shareholders could not hope for better news than this bid from Atos," said Gregoire Laverne of Roche-Brune Asset Management, which sold its Gemalto shares a year ago.

Atos's offer of 46 euros per share, reflecting a 42 percent premium to Monday's closing price, is "very generous", Laverne added.

Still, other analysts and investors said there was scope for an increase.

"It's possible that Atos raises its bid to win the backing of all shareholders," said Xavier de Buhren, an asset manager at Mirabaud AM. "It's clearly an opportunistic transaction," he said.

Atos is aiming to generate cost savings in line with ones generated when it bought computer company Bull in 2014. This represents savings in the range of 4 to 6 percent of Gemalto's annual revenue, or about 150 million euros, de Buhren estimated

Analysts at Oddo and UBS also saw room for a price increase, with the latter putting a price tag on Gemalto of 49 euros a share.

BPIFRANCE WELCOMES TIE-UP

France's state-backed investment bank Bpifrance, which owns 8.3 percent of Gemalto, welcomed the announcement of a tie-up with Atos.

"We see in principle very favourably the consolidation of two French players in the French technology," a spokeswoman for Bpifrance said.

In a call with analysts, Atos chief financial officer Elie Girard said that Gemalto's profit margins could reach the "mid-teens" levels, or around 16 percent, in 18 to 24 months, compared with 6.7 percent in the first half of 2017.

CYBER SECURITY DEMAND

Atos said the combination with Gemalto would allow Atos to strengthen its position in so-called Internet of Things sector of internet-connected machinery and household devices and broaden its payment and security services, including encryption technologies and authentication systems.

Gemalto has developed electronic passports with biometric features that are used by 30 countries. It has also developed software for digital banking and data encryption for companies, according to its website.

Its customers include U.S. telecom operator Verizon and online retailers Amazon and Alibaba.

The acquisition of Gemalto would be Atos biggest transaction in its history.

Gemalto, which employs about 15,000 people, had sales of 3.2 billion euros in 2016.

(Reporting by Mathieu Rosemain. Editing by Jane Merriman)

By Mathieu Rosemain, Cyril Altmeyer and Blandine Henault