The French government is leaning on HP to reduce the 1,240 job cuts it announced last week.
The Prime Minister of France, Dominique de Villepin, is looking to stop HP's plans to cull about 25 percent of the firm's work force there.
Local authorities in France have insisted HP repays the €1.2m (£810,000) it used to start business there seven years ago.
According to the Financial Times, the mayor of Grenoble, where HP's research facilities are located, has visited HP's head office in California in a bid to block the move.
HP has axed just under a thousand jobs in the UK but the government failed to take any action over this. The move was part of a cost-saving exercise that will see 14,500 job cuts worldwide in the company. In total, 6,000 job cuts are planned in Europe.
Gérard Larcher, France's employment minister, is set to meet Francesco Serafini, HP's senior vice-president, on Monday next week for negotiations over the proposed job cuts.