* Protest is third in a year since Macron became president
* All unions back protest, citing defence of public service
* Reforms under Macron include 120,000 civil service job cuts (Adds clashes in Paris, strike impact, arrests)
By Sophie Louet and Bate Felix
PARIS, May 22 (Reuters) - French police and protesters clashed in Paris on Tuesday after unions, angered by years of public sector pay curbs and President Emmanuel Macron's economic reforms, urged state employees to stop work on and join nationwide street protests.
It is the third time that labour unions have sought to stage a nationwide show of strength in such a way since Macron began his five-year term in May 2017.
Reuters television images showed riot police charging at protesters with batons in central Paris, firing stun grenades and tear gas. Some protesters destroyed two shops and a bus stop. Police said 20 demonstrators were arrested.
Around 15,000 people demonstrated in the capital, compared with 49,000 during a similar protest in March, authorities said.
The previous round of protests two months ago drew some 320,000 people in all into the streets.
But union officials say the strike wave, unlike pre-Macron versions that successfully torpedoed attempts to liberalise the economy, appears to be losing steam with more and more workers doubting they can force government to change course.
Macron, 40, has shown no sign of surrender so far.
Tuesday's call came from all of the large labour unions plus many smaller ones and involved organisation of street rallies in about 140 cities, towns and villages across France.
Postal workers, air traffic controllers, state teachers and public administration workers were urged to quit their posts and join marches to denounce what the unions say is an erosion of spending power and the public service itself under Macron.
French electricity grid operator RTE said the strike reduced nuclear electricity generation by 2 gigawatts as several nuclear reactors operated by state-controlled utility EDF were forced to cut production due to the strike.
A spokeswoman for French EDF said around 15.5 percent of the company's staff participated in the strike.
One catalyst for union anger is a proposal to end certain sick leave perks and cut 120,000 government administration posts. Also on the cards is an increased recourse to contract hiring rather than the job-for-life recruitment that is standard in the French civil service.
In all, France has about 5.7 million employees in government administration, state agencies, schools and hospitals.
The latest protest dovetails with one specific to France's national railways: services have been disrupted for several days each week since early April by strikes over plans to end the SNCF train company's monopoly, and with it the hiring of rail workers on contracts more protective than for other sectors.
"We're demonstrating in defence of a public service that is there to serve everyone, wherever in the country they live," Philippe Martinez, head of the Communist-linked CGT union, told RTL radio. (Additional reporting by Emmanuel Jarry and Caroline Pailliez Writing by Brian Love Editing by Mark Heinrich)