Bouygues Telecom said its offer, which includes €10.5bn in cash and 46% in new capital, would involve no forced redundancies and would "revitalise" employment in France's telecommunications sector.
The new company would be floated as soon as the merger is completed.
Vivendi would then be offered the opportunity to monetise a further 15% of the capital and would be free to sell up at any stage.
Bouygues Telecom predicted the deal would generate around €10bn in synergies, 80% of which would be achieved in three years.
Post-synergies, it estimated SFR would be worth €19bn.
"This is the best project for French consumers, French infrastructure, and the shareholders of Vivendi and Bouygues," said group finance director Philippe Marien.
If approved by anti-trust regulators, the new company would potentially create a phone carrier that would rival market leader Orange.
Shares in France's largest mobile network jumped on Thursday after Orange said its net profit more-than doubled to €1.9bn last year, up from €820m in 2012.
Financial director Gervais Pellissier said on a conference call the rise was driven by the evolution of telecommunications asset prices, which has helped to reduce Orange's impairment charges.
It also comes amid a wave of consolidation in France's telecommunications sector.
Earlier this week media agencies reported Altice, the parent company of cable operator Numericable, has also made a bid for SFR valuing the company at around €15bn. Altice has made no public statement on the reports.
Bouygues Telecom said its proposed merger with SFR would create the largest mobile network and second-largest fixed network in France. It also pledged to double investment in France's optical fibre network to €400m a year.
Marien also pledged to protect SFR employees during the merger.
"At this stage, we have no plans to make any forced departures," he told AFP "History shows that when Bouygues makes a commitment, it sticks to it," he added.
Source: AFP via I-Net Bridge
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