PARIS (Reuters) - Two hard-left trade unions led protests across France on Tuesday against labor law reforms backed by mainstream unions to give firms more flexibility to weather economic downturns.

Several thousand people marched through Toulouse, Strasbourg and Rouen, with one banner deploring a "criminal" labor accord, while small-scale transport, port and power sector strikes caused minor delays and disruption.

Other protesters began gathering in central Paris for a 2 p.m. (1300 GMT) march likely to be seen as a barometer of opposition to a reform that Socialist President Francois Hollande's battle says is vital to restoring the competitiveness of French industry.

Signed by mainstream unions in January after lengthy talks with employers, the "flexicurity" accord means more job security for workers on short-term contracts, but makes it easier for firms to put staff on shorter hours if orders dry up. It also gives them new rights to dismiss any who refuse to participate.

The hardline CGT and FO, backed by two smaller unions, had called for protests in some 200 towns. The Paris march was due to head to the Socialist-controlled National Assembly, which is set to pass a law based on the accord next month.

Opposition to the deal, which Hollande hopes will stem a rash of industrial layoffs and ease double-digit unemployment, has become a common cause for two unions who are traditionally enemies. Hard-left lawmakers also oppose the reform.

"This is a dangerous deal," FO leader Jean-Claude Mailly told France Inter radio in a rare joint interview with CGT leader Bernard Thibault. "When we agree on something, we fight together."

A CGT spokeswoman said the union opposed all the points in the labor accord, and that it threatened job security.

Waning competitiveness compared to low-wage countries has pulled down French exports over the years and caused the loss of tens of thousands of jobs, helping to send unemployment above 10 percent.

The economic gloom has knocked Hollande's approval ratings down as low as 30 percent in the months since he was elected last May pledging to restore jobs and growth.

The changes will also seek more flexibility from workers if they are asked to relocate to match fluctuations in demand.

French media reported minimal delays to some flights out of Paris and no cancellations. There was minor disruption of some underground metro services in the capital. Action at power plants had no impact on electricity supply.

The bill, which Hollande wants to be enacted in May, will be presented at a cabinet meeting on Wednesday.

(Reporting by Catherine Bremer, Nicholas Vinocur and Michel Rose; Editing by Alistair Lyon)