Although French unions have called for action to be stepped up as the Euro 2016 football tournament approaches, the government was hoping last week's fuel crisis would not be repeated.
The government insisted that the situation would improve on Monday for motorists who have been forced to queue for petrol and have been restricted in how much they can buy in many parts of the country.
"There will be petrol. Things are getting better although we need to stay on our guard," government spokesman Stephane Le Foll told France 3 television.
Le Foll said the figures for the number of petrol stations hit by shortages were improving while on Saturday the transport secretary Alain Vidalies said "the situation had returned to normal in many regions, while in others we remain very attentive".
While parts of the country have been badly hit by shortages and motorists have had to search for petrol stations with fuel, most have simply had to put up with queuing for fuel.
On Sunday in Paris, motorists were still forming queues to get into some petrol stations but at one outlet in the 19th arrondissement the waiting time appeared to be not longer than 10 to 15 minutes.
Riot police on Friday cleared all the remaining blockades at fuel depots, allowing more supplies to reach petrol stations. One depot remains on strike.
On Saturday Prime Minister Manuel Valls tried to ease the concerns of oil and transport chiefs when they met for talks on Saturday.
Valls vowed to continue to dismantle any blockades around fuel depots and refineries.