France Telecom owns UK mobile operator Orange
France Telecom has proposed a merger with Teliasonera but its proposal has been rejected by the Swedish telecoms firm as "significantly" too low.
The French firm stopped short of making a formal offer, suggesting a cash and stock deal at about a 39% premium to Teliasonera's current share price.
France Telecom had said in April it was in exploratory talks with its rival.
If a deal did go ahead, the enlarged telecommunications operator would be the world's fourth largest.
The merged firm would have about 237 million subscribers, France Telecom said.
It added that together the two firms' "combination of nimbleness and scale" would produce benefits including "advantageous partnerships" with software, hardware, content and advertising providers.
Teliasonera shares rose by about 7% in early Thursday trading as investors looked for the French firm to up its proposed offer.
But France Telecom's chief executive Didier Lombard said that raising its offer was "out of the question".
Buying Teliasonera would be France Telecom's biggest deal since it bought Orange for £27.8bn ($55.1bn) in 2000.
France Telecom's European expansion in the 1990s resulted in a huge debt burden.