Radwanska, who was seeded 14th at Roland Garros, has dropped out of the top 10 this year after a poor run of results and her struggles continued against Beck, who is ranked 81st in the world.
The pair’s previous meeting had resulted in a 6-0 6-0 win for Radwanska but the Pole was unable to repeat the feat, and it is Beck who goes through to the second round.
“That was two years ago and different conditions so we shouldn’t really compare,” Radwanska said.
“It was a really strange match. I started pretty slow and it was too late in that first set.
“I was much better in the second set. I thought I was still playing my game in the third set, but it just went too fast the other way.
“The clay season is not really my favourite one, and I guess it’s not getting better, even when I’m really trying to do everything.
“I just want to forget about that and focus on grass now.”