The improved bid has increased to €11.3 billion, and reduces the stake Vivendi would retain to 43%, down from 46%.
The initial offer made by the operator included €10.5 billion in cash and ownership of 46% of the new company after a planned spin-off, which values SFR at €14.5 billion before synergies.
Experts are predicting that Bouygues could face regulatory hurdles as the acquisition of SFR would create a dominant player in France.
A rival bid was also been prepared by cable operator Numericable, owned by billionaire Patrick Drahi, which values SFR at approximately €14.75 billion.