Mr. Montebourg wanted a "win-win partnership" that left each side with a 50% stake.
Maurice Taylor made the claims in a letter to France's minister for industrial recovery, Arnaud Montebourg.
Jean-Louis Borloo, a conservative politician and a former environment minister, also supported Mr Montebourg's efforts.
The Mittal family said they were "extremely shocked" by Mr Montebourg's attacks on the steelmaker.
That prompted Mr. Montebourg in January to beseech Mr. Taylor to return to the table.
The war of words is the latest involving Mr. Montebourg and a foreign company.
France's minister for industrial recovery, Arnaud Montebourg, accused the steelmaker on Monday of "lying" and "disrespecting" the country.
Titan pulled out of negotiations in September, citing the "heavy social climate" in France, said a spokeswoman for Mr. Montebourg.
Arnaud Montebourg, a Socialist deputy, accused the rock star of blackmail and demanded repayment of any local subsidies received on tour.
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"We no longer want Arcelor Mittal in France because they didn't respect France, " Arnaud Montebourg told French business daily Les Echos.
The problem "isn't the furnaces in Florange, it's Mittal", said Mr Montebourg.
As a result, Mr Montebourg has said he is exploring how to seize the entire Florange site should Mr Mittal refuse his demands.
According to the French newspaper, Mr Montebourg's idea "would be a partnership with a minor manufacturer, the time to stabilise activity" in Florange.
This is not the first row that Mr Montebourg has been involved in since the Socialists took charge of the presidency last summer.
Hollande and Montebourg talk up small enterprise, but it's self-defeating to treat those companies as rare and precious flowers in need of state coddling.
The real revelation of the primary has been the energetic clarity of two younger, less-known candidates: Arnaud Montebourg (aged 48) and Manuel Valls (49).
It's revealing that Mr. Montebourg referred to Dailymotion as a startup.
Mr. Montebourg hit back in his response to the U.S. businessman.
But other motions are being prepared, for instance by Arnaud Montebourg and Vincent Peillon, two young radicals, as well as by Henri Emmanuelli, a left-wing firebrand.
Mr Montebourg's promise of a golden tomorrow, which he makes with aplomb as part of a makeshift stand-up act in the street, is proving more seductive.
Mr Montebourg has duly toured the country promising the impossible.
Taylor, who is nicknamed "The Grizz", wrote the no-holds-barred letter to French Industrial Renewal Minister Arnaud Montebourg to explain why his company wouldn't buy part of an ailing Goodyear factory in Amiens.
His pledge to save industry, by giving Arnaud Montebourg, an anti-globalisation politician, the job of preventing closures, is looking empty as manufacturers line up to close factories and slam high labour costs.
Meanwhile, a maverick Socialist member of parliament, Arnaud Montebourg, is gathering his colleagues' signatures in a surely futile, but nonetheless headline-grabbing attempt to change the constitution so that a sitting president can be made to answer questions from the magistrates.
The pair also neatly embody the stark choice that the French left has never really confronted: between a return to the old-style protectionism that Mr Montebourg calls deglobalisation, and a recognition that the debt crisis and globalisation have changed the rules, as Mr Valls urges.
Mr. Montebourg's full title is "Minister of Industrial Renewal, " but hardly a month seems to pass without another story about a plant shutting down, or Mr. Montebourg threatening a CEO for threatening to shut down a plant, or begging a CEO (sometimes the same one) to stay in France.
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