Bouygues said the deal had "significant execution risks" related to French competition law.
Also, France's government had voiced concerns about employment threats and higher consumer prices should the competition be reduced.
A merged firm would have leapfrogged Orange to become France's largest mobile phone company.
Altice wanted to combine Bouygues' mobile, internet, and fixed phone businesses with those of Altice division Numericable-SFR.
In its statement, Bouygues also said its "strong and lasting competitive advantage" derived from its range of mobile frequencies and 4G network left it capable of expanding its business on its own.
On Monday, France's Economy Minister Emmanuel Macron said further consolidation in the telecoms sector was "currently undesirable".
"Now is not the time for opportunistic tie-ups which may be of interest to some people but which are not in the public interest," he added.
"Jobs, investment and better customer service are the priorities."
The rejection of the bid is likely to be a setback for Altice's acquisition-hungry owner,  Franco-Israeli tycoon Patrick Drahi.
He is behind a series of telecoms and media acquisitions, and in 2014 purchased SFR and later merged it with cable operator Numericable.
French telecoms group Bouygues has rejected unanimously a near €10bn takeover offer by rival group Altice.