The slightly "archaic" style of this story is not that of Pushkin himself, but of Belkin, a fictional author of "Tales of Belkin". As a matter of fact, this style is more ironic than archaic and a part of the image of Belkin made by Pushkin. As a Russian, I think that the language used in this story is 99% modern Russian. Combined with that the story is fascinating itself I can recommend it for parallel reading even if your level of Russian is below intermediate. Remember, parallel reading doesn't require you to memorize everything you read.
P. S. To be honest, the *very* first book in English and Russian I have finished was "Master and Margarita" by Bulgakov, 17500+ fragments (English translation by R. Pevear, 1997). To my shame, I didn't know that creating a derivative book was violating copyrights of the original authors and translators. When I got to know this I had to remove that book from the list (imagine how much work has been done in vain).