Total said preliminary operations to restart its Normandy, Grandpuits and Feyzin refineries were underway on Monday.
Donges refinery on France's western coast was still being blocked by about 30 militants from the CGT union.
FACTBOX-Strikes hit French oil refinery network.
With around 400,000 tonnes of diesel waiting in tankers outside French ports or en route, it remains unclear how much additional imports will be required in the coming weeks, traders said.
Demand in the region was weak as stock level remained high, traders said.
Higher global refining capacity in the summer months is expected to put new pressure on margins, particularly diesel cracks, Morgan Stanley said.
Around 2.7 million barrels per day of refining capacity is set to return from maintenance globally from May to June, according to Morgan Stanley.
An additional 2 million bpd will return in July.
Egyptian General Petroleum Corporation (EGPC) issued tenders to buy 2 cargoes of 0.1 percent gasoil into the ports of Dekheila and Suez in June.
GASOIL
There were no 0.1 percent sulphur gasoil barge or cargo trades.
Glencore sold to Total one barge of 50 ppm gasoil traded at discounts of $5.75 a tonne fob ARA to the June Low Sulphur Gasoil futures contract, compared with discounts of $7 a tonne on Friday.
June Low Sulphur Gasoil futures were $3.25 a tonne higher at $446.25 at 1554 GMT.
The June and July contracts were trading in a contango of 75 cents a tonne, unchanged.
The diesel refining margin was at $9.75 a barrel, down from $10.18 a barrel on Friday.
DIESEL
Some 22 diesel barges traded at discounts of $2-$3 a tonne fob ARA to the June diesel futures, compared with discounts of $3.50-$4 a tonne the previous day. Glencore, Shell and Gunvor sold to Vitol, Trafigura, Rolympus and BP.
Glencore also sold to Vitol one cargo cif Hamburg.
JET FUEL
No barges of jet fuel traded.
Vitol sold two cargoes to Shell and BP at $22-$23 a tonne cif Rotterdam above the July diesel futures, down from Friday's trade at $24 a tonne.
FUEL OIL
Barges with a sulphur content of 3.5 percent fuel oil traded at $222.50-$224.25 a tonne fob ARA, compared with $218-$218.50 a tonne the previous day.