The third seed, who reached the quarter-finals at Roland Garros last year, earned a 6-3 6-0 victory on the famous clay in a match that lasted just over an hour.
Zhang failed to hold serve once in the contest, but Radwanska had problems of her own and it was the Pole’s solitary hold that ultimately settled the first set.
Things got worse for the Chinese in the second as the world number three romped to victory in only the second meeting between the pair.
Radwanska has never won a grand slam title – her 2012 Wimbledon final appearance the closest she has come – and she faces the likely prospect of having to get past Serena Williams if she is to end that run in Paris.
Next up for Radwanska will be a meeting with either Mathilde Johansson of France, or Czech Karolina Pliskova.
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