By Sudip Kar-Gupta and Gwénaëlle Barzic

Elliott has built up a stake of just over 10% in Altran through equity derivatives. It has already said it thought software consultancy Capgemini's 14 euro per share, or 3.6 billion-euro ($4 billion) bid for rival Altran, was too low.

It argued on Wednesday that other deals in the sector had carried higher premiums.

"Elliott believes the offer price neither reflects Altran’s intrinsic fair value, nor an adequate premium for control", Elliott said in a statement.

Capgemini immediately rejected Elliott's statement.

The hedge fund, which has built its reputation for activism in the United States, caused waves last year when it revealed a stake in French drinks maker Pernod Ricard.

In France, it is not unusual for big company stakes to be held by families or even the government and in the past that has proved a deterrent to activist investors. But some funds are starting to look past these, and are beginning to disrupt what they perceive as a cosy business environment.

Capgemini's Chief Executive Paul Hermelin told Reuters in an interview this week that the software company would stand by its price tag. He reitered that view on Wednesday in comments to French news site Boursorama.

He had also expressed confidence that Capgemini would manage to get 50.1% Altran shareholders behind the deal.

There is nothing to stop Elliott from increasing its stake in Altran, a source familiar with the matter said, although it is not clear whether it would.

Elliott did not say what price it was looking for, but the fund considers that at 20 euros per share, the deal would still create value for Capgemini, the source added.

Elliott - which broadly backs a combination of Capgemini and Altran - has also taken aim at Altran management's role in validating the offer price, alleging a potential conflict of interest.

Chief Executive Dominique Cerutti had a bonus payment linked to former shareholder Apax Partners selling its stake at a certain price, regulatory filings show. Apax agreed to sell its remaining investment in Altran to Capgemini for 14 euros a share in June.

A spokeswoman for Altran said the firm had followed the law and regulations in full throughout the bidding process, which got the green light from France's financial regulator.

In late session trading, Altran shares were little changed at 14.07 euros in Paris, while Capgemini shares were down 1%.

(Additional reporting by Sarah White; writing by Matthieu Protard; editing by Elaine Hardcastle)

By Sudip Kar-Gupta and Gwénaëlle Barzic