June 6 (Reuters) - Bouygues Telecom, Orange and Free-iliad Group have signed a memorandum of understanding with Altice France to buy telecoms operator SFR for €20.35 billion ($23.44 billion), including debt, the companies said on Saturday.     The Bouygues-led consortium had said on Friday that, in view of the progress made in the negotiations, the parties had given themselves another 48 hours to finalize the agreements.

Last month, Altice France extended the exclusivity period for talks with the consortium until June 5 from a prior deadline of May 16, after the three operators raised their offer in April from around €17 billion.

If approved by regulators, the acquisition would rank among the biggest European telecoms deals in recent years.

A break-up of SFR would reduce the number of mobile network operators in France to three from four, setting up a key test of antitrust authorities' willingness to allow consolidation in Europe's crowded telecoms market.

Orange Chief Executive Christel Heydemann said in April that the company had begun regulatory discussions ahead of the deal and cited behavioural remedies as one possible route to approval.

Under the terms agreed, the split of the price between buyers remains at about 42% for Bouygues Telecom, 31% for the Free-iliad Group and 27% for Orange.    The MoU also provides for break-up fees varying between €0.1 billion and €2 billion.

($1 = 0.8681 euros)