Prior to the rise of National Socialism, the swastika was a common graphical motif, found in everything from Indian blankets to architectural details. (My wife's grammar school featured a nice tiled row of swastikas when she was young. I doubt very much they're still in place.) The prominence of the design in many cultures with a wide geographical and historical spread is actually easily explained: it's a common repeating pattern that naturally forms in certain types of basket weaving.
When Hitler adopted the "crooked cross" as the Nazi Party symbol, the once-harmless design took on sinister connotations which it shall never shed. I read some speculation online that these cards were produced by USPC for export to Nazi Germany, which is absurd on various levels. German card design is different, for one thing, and they had no need to import cards. The idea that Nazi Germany would have imported French-suited playing cards from the US is just silly.
Here's the best quality picture I can find, and this one came from an auction that I lost. If I can get hold of a better quality version, I'll post it at a later date.