Several hundred tractors blocked access roads to Lyon on Thursday morning, while others blockaded the A20 motorway, an important route for road freight from Spain and the south-west to Paris and the north.
Protests, often targeting supermarkets, have spread south from Normandy, where they were concentrated earlier in the week.
Some, such as the blockade of the Channel port of Caen, were lifted on Wednesday.
The main farmers' union, the FNSEA, dismissed the aid package announced by the government on Wednesday, as "insufficient" and its leader, Xavier Beulin, predicted more disruption over the next two or three days.
While saying he understood their "distress and despair", Prime Minister Manuel Valls appealed to the farmers "not to punish the country, people going on holiday, the economy" ahead of a weekend when many French people start their summer vacation.
But he also insisted that it was "essential" that beef prices rise.
Hollande, who was to meet farmers in the Burgundy city of Dijon on Thursday, called on abattoirs and food-processing companies to "account for themselves" after a mediator's report identified them as the biggest culprits in the failure to keep a June agreement to raise meat prices.
Right-wing opposition MP Christian Jacob, a former farmers' union leader, on Wednesday slammed the aid package, calling it a "masquerade" and a "public relations exercise".
Valls hit back on Thursday, accusing him of "populism".
Former president Nicolas Sarkozy judged it "inadequate for the crisis facing of French agriculture".