* Unions to strike in two-day waves over three months
* Railway traffic seen widely disrupted on Tuesday
* Polls show majority of French backing SNCF reform (Adds union comment, details of disruption)
PARIS, April 3 (Reuters) - French railway services were decimated on Tuesday, the first day of rolling strikes which are due to run for months in a serious test for President Emmanuel Macron's resolve to modernise the French economy.
The four main rail unions have called two days of strikes in every five days for the next three months to protest against a shake-up of the national SNCF rail monopoly before it is opened up to competition as required by EU law.
The last time a French president squared off against rail unions over workers' benefits it ended badly. The strikes of 1995 paralysed France and forced prime minister Alain Juppe to pull the reforms - a defeat which ultimately prompted Juppe to quit.
"We're defending the French public service, not just rail workers," said Emmanuel Grondein, head of Sud Rail, one of the four unions behind the industrial action.
The unions are somewhat weaker than in 1995 and divided in their response to Macron's social and economic reforms. More than half of French people view the strikes as unjustified, according to an Ifop poll published on Sunday.
After an Easter holiday weekend, the SNCF was faced with one of the biggest strikes in years, with nearly one in two staff off work.
Commuter lines into Paris were slashed and only one in eight high-speed TGVs were scheduled, the SNCF said. Bus services into the capital were overwhelmed, with BFM TV reporting that police were called to remove people who overcrowded one bus.
International train services also face disruption: no trains were set to run between France, Switzerland, Italy and Spain. One in every three trains to Germany was to operate, while the Eurostar service connecting London, Paris and Brussels was down to three out of every four trains, the SNCF said.
SNCF boss Guillaume Pepy, who backs the reforms, has warned of widespread disruption.
"I want to be very clear ... the strike action will no doubt be widely adhered to and his going to make the lives of a lot of people very difficult," he said in a radio interview.
Macron wants to transform heavily indebted SNCF into a profit-maker. Unions say he is paving the way for privatisation.
If Macron triumphs over the unions, it will set the tone for other key reform plans including revamping the education system and overhauling pensions. He has already stared them down over easing labour laws.
SNCF workers fear they could lose job-for-life guarantees, automatic annual pay rises and a generous early retirement policy.
Borne has sought to ease tensions with assurances that current SNCF employees that have to move to a competitor in the future would keep most of their advantages.
The Communist-rooted CGT wants the strike to spread beyond the rail sector. Energy sector workers plan to join the strike action from April 3 to June 28, to protest against the planned liberalisation of the power sector.
The CGT has called for public and private sector workers nationwide to strike on April 19, but in a sign of union division, private sector unions have so far declined. (Additional reporting by Brian Love and Bate Felix; Editing by Richard Lough and David Evans)