The Springboks started nervously but scored four tries as centres Jesse Kriel and Jan Serfontein also crossed over, to go with a penalty try.
France, who had made 10 changes from the side that played Wales in their final Six Nations match in March, were in the game until the final quarter as centre Henry Chavancy and replacement scrumhalf Baptiste Serin crossed the tryline for the visitors.
There were green shoots of recovery for the Boks after their disastrous 2016 season in a game watched by just 29,313 fans.
"I am really pleased, we are moving in the right direction," Bok coach Allister Coetzee said. "It's step one of 13 games this season but our attack, defence and the kicking game were all good.
"We are not there yet, we must acknowledge that the French played without a lot of their leading players and still put us under pressure at times."
The hosts' opening try came as fullback Andries Coetzee found a gap and sprinted clear, with the ball reaching Kriel to score for a 13-0 lead.
Chavancy was able to dot down for the French after good work from wing Yoann Huget as his chip was missed by Coetzee in the goal area.
France closed the gap to two points when Serin darted over from close range.
But minutes after the introduction from the bench of Frans Steyn for his first test since 2012, the centre provided a perfect grubber kick for Courtnall Skosan to chase.
The wing could not reach it but was adjudged to have been held back by France fullback Brice Dulin and a penalty try was awarded.
It proved a turning point in the game, but France coach Guy Noves had no complaints.
"There's not much to say, the referee was logical in his decision," Noves said. "Our playing level was a lot less than I expected, we missed a lot of tackles."
A well-worked routine from the line-out saw Cronje sprint clear to score shortly afterwards, before Serfontein added a fourth try.
The second test will be played in Durban next Saturday, with the final match in the series at Ellis Park in Johannesburg on June 24.
(Editing by Clare Fallon)
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