Hauliers have been active for several days, using vans to slow traffic on motorways around Paris and cities like Lille, Rennes and Lyon.
Unions have called on drivers to block busy roundabouts, oil refineries and major distribution centres.
Security van drivers, vital for keeping cash point machines stocked up, have signalled that they will also join the strikes.
Twelve French Oil refineries have been hit since Monday, according to the CFDT union. Petrol distribution centres across the country, especially at northern ports, are subject to strikes and blockades by lorry drivers.
Many filling stations are closing as stocks dry up, with diesel in particular running short, especially in Paris and Nantes.
Some 260 secondary schools offered a “reduced service” on Monday, expected to continue Tuesday. Police had to step in after rioting students went on the rampage, some setting fire to cars, in Nanterre and Lyon.
A school in Le Mans, in north-western France, burned down in the early hours of Tuesday after an apparent arson attack, but it was unclear whether it was linked to the protests.
Public transport across France remains extremely affected, although there is a minimum service running on most lines. In Paris, the metro, tram and bus services are almost normal while some RER lines (covering the greater Paris area) are running a reduced service. The RER B line serving the main Paris airports of Charles de Gaulle and Orly has been particularly hit.
Public transport is also affected in Lyon and Toulouse. Across France, TGV and inter city trains are running a severely reduced service while international train services (Eurostar and Thalys) are unaffected.
Airports are affected as air traffic controllers strike, with mostly short-haul domestic and European services affected, although long-haul international are mostly continuing as usual.Strike action for airport staff will continue on Wednesday.