The latest protest comes after a week of demonstrations against a fall in food prices that has brought farmers to the brink of bankruptcy, and which they blame on foreign competition, as well as supermarkets and distributors.
Farmers have so far blocked motorways with their tractors, dumped manure in cities and let pigs loose in supermarkets.
The main farmers' union, the FNSEA, has dismissed an emergency package worth 600 million euros in tax relief and loan guarantees, calling it "insufficient".
From late Sunday, farmers in the northeastern Alsace region have used tractors to obstruct six routes from Germany in a bid to stop trucks crossing the Rhine carrying agricultural goods. The blockage has forced at least a dozen trucks to turn back at the border.
"We let the cars and everything that comes from France pass," Franck Sander, president of the local branch of FDSEA, told French news agency AFP, adding that more than a thousand agricultural workers were taking part in the roadblocks.
Meanwhile, around 100 farmers ransacked dozens of trucks from Spain on a highway in the southwestern Haute-Garonne region, threatening to unload any meat or fruit destined for the French market.
Hollande said Monday that the farmers "should know that, protests or no protests, we are on their side."
"We must act. Our minister of agriculture has ensured that we can put the necessary pressure on distributors, processors, packers," the president said.
Speaking to Radio France Inter on Monday, Agriculture Minister Stéphane Le Foll reminded farmers that there is a similar crisis in other European countries.
"France and French producers also export to these countries," he said, adding that "we must respect that in Europe, we try to find solutions at the institutional level.”
The European Union’s Council on Agriculture will meet 7 September in Brussels to discuss the crisis.
Hollande assured that at the meeting, "we will continue to put pressure."
Sander of the FDSEA told AFP that governments must find "concrete solutions to end the distortions of competition" with farmers in neighbouring countries, lambasting the differences in the cost of labour and disadvantage of French farmers.
The blockade at the German border was lifted after union representatives for farmers met with government officials in Strasbourg Monday afternoon, but they swore to remain on alert "as we wait for results."