The transport strike adds to problems still being caused by last week's blockade of fuel depots which left motorists queuing at many petrol stations.
The rolling train strike called by the powerful CGT union is expected to affect around half of national and regional train services.
That will be followed by a strike on the Paris Metro network from Thursday and Air France pilots have voted in principle for a lengthy strike at some point in June, when Euro 2016 is in full swing, AFP reported.
The protests and strikes have cast a shadow over the European football championships, which are expected to attract millions of foreign visitors to France when the tournament kicks off on June 10.
Neighboring Belgium also faced growing disruption Tuesday from a public sector workers' strike.
But despite three months of stoppages and sometimes violent demonstrations against labor reforms, Hollande again refused to bend to the unions' demands to scrap the legislation.
The measures, which would make it easier to hire and fire employees, "will not be withdrawn", a defiant Hollande told Sud Ouest newspaper.
"The text assures the best performance for businesses and offers new rights to employees," he said.
"I consider it necessary to see it through to its conclusion."
Hollande said that despite the predicted transport chaos, the biggest threat to Euro 2016 "remains terrorism".