Berendsen, which called the Elis approach "opportunistic", said it was investing 450 million pounds to expand in Europe and to replace plant and machinery in Britain.
"The board of Berendsen unanimously concluded that the revised proposal very significantly undervalues Berendsen and its prospects," it said in a statement, adding it did not see a basis for further discussion.
Elis said it was offering 440 pence in cash and 0.426 new Elis shares for each Berendsen share, valuing the British firm at about 2.05 billion pounds. It said this valued each Berendsen share at 11.73 pounds, after an April offer had valued each share at 11.00 pounds.
"This looks an attractive pricing for the group," RBC Capital Markets analyst Andrew Brooke said, citing concerns about Berendsen's capital expenditure plans and its ability to turn around its operations in Britain.
Berendsen, which posted annual revenues of 1.1 billion pounds for 2016, said in March its profitability in 2017 would be weighted to the second half as profits in the first half would be hit by its legacy operations in Britain, which account for about one third of its business.
The French group said it was approaching Berendsen's shareholders, after the firm's board rejected both its proposals. It said Berendsen shareholders would end up with about 35 percent of the combined group.
Berendsen shares were up 25 percent at 10.75 pounds at 0819 GMT while the Elis shares were down 4.8 percent at 19.025 euros.
(Additional reporting by Sudip Kar-Gupta; Editing by Greg Mahlich and Edmund Blair)
By Wout Vergauwen