This represents the lowest level of support since the launch of the strike polls in mid-March, according to the survey organisation Ifop.
A clear majority of French (62 percent up one percent compared to the previous poll) want the government to go "to the end of the reform of the SNCF as it was announced, without giving in to mobilizations and strikes". That figure was only 51 percent at the end of March.
Furthermore, 74 percent (-4 percent) think that the government will carry out its reform to the end.
The survey was conducted online on April 26 and 27 with a sample of 1,000 people, representative of the French population aged 18 and over.
Unions accuse Macron, a centrist ex-investment banker, of seeking to "destroy the public railways through pure ideological dogmatism".
They fear that plans to turn the SNCF into a publicly listed company, even with the state owning 100 percent of shares, could eventually lead to the rail operator being privatised -- something the government denies.
The rail strikes are being seen as the biggest challenge yet to Macron's sweeping plans to liberalise the French economy and make it more competitive.
He managed to pass controversial labour reforms in October, but the length and severity of the rail strikes are already earning comparisons with British prime minister Margaret Thatcher's showdown with coal miners in 1984.
The industrial action is a major test, too, of how much influence France's once fearsome unions -- whose membership has plunged to just 11 percent -- still carry.