* Protest is first test for Hollande on debt control
* Union says demonstration is first of many
* Protest comes as France seeks to slash debt (Updates with estimate on number of strikers)
By Brian Love
PARIS, Jan 31 (Reuters) - Tens of thousands of public sector workers marched through Paris and other French cities on Thursday to demand better pay in the first street challenge to President Francois Hollande's deficit cuts since he was elected last May.
Under pressure to curb spending and reduce a debt swollen by the economic downturn, Hollande's Socialist government has refused to lift a public sector pay freeze imposed by his conservative predecessor, Nicolas Sarkozy, in 2010.
The CGT labour union said 150,000 people took to the streets nationwide. Thousands of state employees stayed off work.
"This is a first step," Baptiste Talbot, spokesman for the public service branch of the CGT, told reporters in the French capital as a modest crowd marched under drizzly skies.
Public services minister Marylise Lebranchu stood firm, saying the 5.2 million people on the public payroll - who according to polls tend to vote more than the national average - had an interest in helping with cost control.
"If deficits are too big and we lose some financial independence, this will be painful for public service staff as well," she said, using the government's argument that if France does not clean up its public finances it risks higher borrowing costs on financial markets.
France's public sector wage bill is expected to total 80.6 billion euros in 2013, a year when the government is looking to cut its deficit from 4.5 percent to 3 percent of gross domestic product, or by roughly 30 billion euros ($40.7 billion).
The government reported a relatively small average strike rate, saying less than 7 percent of public servants stopped work. That rate was slightly higher among workers in state hospitals and schools.
More than 1 in 10 state-employed teachers stopped work, but no schools shut, the education ministry said.
Thierry Lapaon, the man taking over shortly as leader of the CGT union, one of the two biggest, said state employee wages had on average fallen 13 percent in the past decade and the situation was becoming untenable for many low-grade employees.
His union had called for people to vote for Hollande last May but had seen no improvement under the first Socialist president in almost two decades, he told RTL radio.
"People were fed up with Nicolas Sarkozy, his policies and his government. But what's changed since? Not a lot as far as wage-earners are concerned," he said.
Lebranchu, who is due to hold talks with the unions on Feb. 7, said a 1 percent rise in the index used to determine public sector pay would cost around 700 million euros.
The CGT union said it would push for further protests if the minister did not produce "genuine answers" at the next meeting. ($1 = 0.7370 euros) (Additional reporting by Gerard Bon and Sophie Louet; editing by Mark John)