Interesting word

Saw the impeccable in writing for the first time today and went to look
it up. The result from Online etymology Database at etymonline.com:

impeccable


1531, "not capable of sin," from M.Fr. impeccable (15c.), from L.
impeccabilis "not liable to sin," from in- "not" + pecare "to sin," of
unknown origin.

Now I wonder, the verb pecare, has this any connection to the german
word Pech which roughly means sin, shame or pity? Is the german word
dependent on the latin word or the other way around?

Carl Hult