Publicis shares fell as much as 5 percent in early Monday trade. They were down 2.6 percent at 1128 GMT, the biggest fall on France's blue-chip CAC 40 index.
"A good asset at a steep price," said Exane BNP Paribas analyst Charles Bedouelle of the deal, adding it would "likely push back (Publicis') cash return story by two years."
UBS analyst Tamsin Garrity said Publicis had been under pressure from investors to return cash, and was expected to announced share buybacks at a strategy day on Friday.
"The acquisition of Sapient makes such returns unlikely," she added. Garrity has a neutral rating on Publicis shares.
Levy defended the decision, saying the company would generate more value in the long term by buying Sapient rather than buying back its own shares. He pledged to update investors on his approach to dividends and buybacks sometime in November.
"This operation is extremely important for securing the future of Publicis," Levy said. "It is far better to invest and deliver a higher growth and higher profits ... which will lead to a re-rating, rather than simply buy back our own shares."
"The deal will create a foundation for accelerated growth" by giving Publicis access to new markets and revenues, he added.
Publicis said the deal would be financed through existing cash and new debt, and would not affect Publicis' credit rating. It did not say when it would add to group profits but forecast 50 million euros ($63 million) in annual cost savings.
'A jilted lover?'
Sapient's sales grew 14.1 percent to 1.1 billion euros last year, far outstripping Publicis' sales growth of 1.2 percent, though the French company had a higher operating profit margin. The U.S-based group earned 63 percent of its 2013 sales in North America and has 13,000 employees, 8,500 of which are in India.
"The risk that growth slows at Sapient is one of the transaction's more important considerations," said Pivotal Research Group analyst Brian Wieser.
He noted the deal gave Sapient an enterprise value (equity plus debt) of around 12 times its forecast earnings before interest tax, depreciation and amortization (EBITDA) for 2015, far above Publicis' current multiple of about 8 times.
Martin Sorrell, the chief executive of Publicis' rival WPP, was even harsher, telling financial blog Business Insider that Publicis had rushed into the Sapient deal to compensate for its botched marriage with Omnicom.
"It looks like the behavior of a jilted lover," he said.
Buying Sapient will speed Publicis' roughly seven year-old effort to earn more revenue from digital advertising, which includes everything from online marketing to brand building on social networks and automatic ad buying for major customers.
Last year, 38.4 percent of Publicis' sales came from digital, and it had been aiming to reach 50 percent by 2018, something that the Sapient deal will make happen immediately.
According to Zenith Optimedia, the digital ad market is expected to grow 17.1 percent this year, driving total ad market growth of 5.3 percent.
Sapient's main SapientNitro unit is a digital agency on a par with Publicis' Razorfish and WPP's AKQA with customers including carmaker Fiat, retailer Marks & Spencer, and consumer goods group Unilever. Sapient also has a technology consulting business serving government and banks, which brings in a third of revenues but is less profitable than the ad business.
Publicis' management and supervisory boards unanimously backed the deal, as did the board of Sapient, which will recommend shareholders tender their shares. As a result, Sapient will be de-listed from the Nasdaq stock exchange.
Sapient boss Alan Herrick will continue to run the company and join Publicis' management team, while Jerry Greenberg, the co-chairman of Sapient's board will join Publicis' board.
The transaction is expected to close in the first quarter of next year. Citigroup has committed to financing the bid.
Bank of America/Merrill Lynch and Rothschild advised Publicis, while Goldman Sachs and Blackstone advised Sapient.