The government now has three weeks to study the offers for stakes worth 13.5 billion euros ($16 billion) at current prices, and try to square its economic patriotism with financial needs.
"Price will be a main factor in the decision, but there is some margin for manoeuvre," said Oddo Securities sector analyst Charles-Edouard Boissy.
The smallest of the three firms, Sanef, attracted three or four bids, there are four or five bids for Autoroutes Paris-Rhin-Rhone and one for biggest firm ASF.
Sanef gained 2.54 percent to 52.55 euros on Tuesday morning, setting a year high, APRR added 2.18 percent to 56.30 euros and ASF was up 1.29 percent to 47.20 euros.
The Finance Ministry said on Monday it had received "several bids" from an original group of 18 candidates, and would now study the dossiers looking at price, social and industrial plans and public services. It expects a decision in early December.
The road sale coincides with the controversial partial privatisation of power giant EDF and follows the recent government decision not to sell part of nuclear firm Areva.
The French state is selling its holdings of 50.3 percent of Autoroutes du Sud de la France (ASF), 70.2 percent of APRR and about 74.3 percent of Sanef to help cut national debt and finance infrastructure projects.
The three firms together with privately owned Cofiroute operate most of the country's 8,000 km (5,000 miles) of main highways. Opposition politicians and some from the centre-right majority have criticised the sale and want the roads to remain in state hands as national assets.
The previous centre-right government shelved a stake sale plan as recently as December 2003.
French construction group Vinci confirmed it made an offer for ASF, in which it has a stake of some 23 percent. "We lodged a bid document that includes financial elements as well as industrial and social chapters," a spokeswoman said. She did not say whether Vinci was bidding alone or with partners.
At Eiffage, an official said the group submitted bids for stakes in Sanef and APRR, with partner Macquarie Infrastructure of Australia. "We're going for the finish line," she said.
Italy's Autostrade had no comment on whether it had presented a firm bid for APRR but Europe's largest toll-road group had lined-up a consortium of French financial firms - CDC, CNP Assurances, AXA, AGF and Predica.
Spanish firms can write down any goodwill on an acquisition more quickly under their tax system than French or Italian companies, which bankers said would allow them in principle to bid higher, and several joined the bidding.
A consortium headed by Abertis bid for Sanef, according to industry sources. The group also included AXA, CDC, Predica and the Peugeot family.
Abertis is bidding for APRR on its own.
Cintra, a unit of Ferrovial, is also bidding for APRR and Sanef with the backing of Caja Madrid and Canadian funds Borealis and Ontario Teachers.
Sacyr Vallehermoso SA unit Itinere still in the race but industry sources could not say whether it bid for one or two firms. FCC announced its withdrawal on Monday, but could jump on board of a winning consortium.