PARIS (AP) _ France's conservative government, faced with a prison system bursting at the seams, decided Wednesday to call on private companies to build, staff and run new penitentiaries.

The plan, devised by Justice Minister Alain Chalandon, was approved by the Cabinet and probably will be presented to a special session of Parliament in January.

Socialist President Francois Mitterrand opposes the plan, but there is nothing he can do to stop the conservative-dominated Parliament from passing the measure.

Opponents of the plan, among them many prison guards, say that the justice system should be left in the hands of the state and that private enterprise should not profit from crime.

French prisons have room for 32,500 inmates, but 48,371 currently are serving time. Chalandon said that by 1989 there may be 65,000 to 70,000 inmates.

Over the past 15 years, Justice Ministry budgets have allowed the construction of an average of 600 new units every year, Chalandon said, adding that at the current rate it would take 67 years to meet the state's needs.

His plan calls for the immediate construction of 15,000 units and of 10,000 units at a later date. Chalandon said work could begin as early as next spring and the initial phase could be completed by the end of 1988.

The government would retain ultimate control over the private prisons and intervene when necessary, he said.

Companies bidding for contracts to build, staff and run prisons must be approved by the Justice Ministry.

Personnel would be recruited by the private companies but trained and certified by the government in the same way as present employees. Certification for private prison personnel would be verified and renewed every five years, and could be revoked at any time.

Chalandon said the government would continue to operate present penitentiaries and continue its own building and modernization program.

In the past, authorities dealt with the problem of overcrowding by granting amnesties and early releases.

''They (the French) are fed up with seeing the release of people who attack or steal from them,'' Chalandon said.

He said the program was ''absolutely indispensable'' for the fight against crime.

Critics, however, questioned whether private companies should profit from crime and said the government apparently gave little thought to alternatives to incarceration as a means of dealing with criminals.

Mitterrand, in expressing his objections, quoted philosopher Alexis de Tocqueville who wrote: ''If it is the business of government to assure the safety of society ... the business of the entrepreneur is to make money. And the government, in dealing with him, must necessarily submit more or less the public interest to private interest.''

Prison guards, initially in favor of the idea because it would ease prison conditions and create new jobs, now oppose it.

The main prison workers union is concerned that those working for the private prisons would not have civil servant status.

In addition, ''the private guards will only have to deal with small-time criminals, and they will work in new establishments with sophisticated equipment,'' said Jacques Vialettes, the union's secretary-general.

''To us will be left the hardened criminals and the most decaying facilities. As to hopes for promotion and transfer, that's ended because the state will create practically no more new establishments,'' Vialettes said.

However, protest strikes by guards on Monday and Tuesday did not attract widespread support.

''We are functionaries,'' said Vialettes. ''If the law is voted and if the Constitutional Council approves, we will obey.''