Conjunctions typically join two clauses (or at least appear at the end of one). Do you have a clause on either side of ものの? You do not, so this can't be the conjunction ものの, and you must be parsing it wrong, as istrasci says.
Instead, you should understand しょうじきもの as a compound word:
- The head もの means ひと 'person'.
- The modifier しょうじき describes what sort of person it is.
So the compound as a whole means 「しょうじきな ひと」.
What does の do, then? It's a type of copula; it does what's traditionally called "apposition". In short, it's saying that the おじいさん and おばあさん are しょうじきもの.
The entire noun phrase しょうじきものの おじいさんと おばあさん serves as the subject of the first sentence. The story introduces these two characters with a brief description. Note that if you want to come up with a translation that makes sense, you should use the entire sentence, including the bit at the beginning you left out (むかしむかし ゆきぶかい やまおくに).