This appears to put an end to the chances of the Vodafone Group acquiring Cégétel, a deal that had been on the table for almost two months.
Vivendi will pay €4bn (£2.55bn) for BT's stake, lifting its share of Cégétel to 70%. Cégétel in turn owns 80% of Société Française du Radiotéléphone (SFR), France's second-largest mobile phone company, which is regarded as the strongest unit in Cégétel. Vodafone owns the remaining 20% of SFR.
Securing control over Cégétel was an essential step, said Vivendi chairman and chief executive officer Jean-René Fourtou. Cégétel is expected to show strong revenue and profit growth over the next three to five years.
Vivendi piled up billions of euros in debt as it grew from a utilities company to a conglomerate active in areas such as media, Internet and telecommunications. It has since been looking to reduce that debt by selling assets.