Does "ducking" have anything to do with a canard?

According to a dictionary of Middle English originally published in 1891, the modern English noun duck originates from Middle English dūke, which is itself a derivation of the Middle English verb dūken, comparable in meaning to our modern verb duck.

The OED entry for canard suggests that the modern usage of canard in the sense of cheating or deception is derived from a more complex metaphor, and seems to have nothing to do with duck in the modern sense of the verb.

Taking these two very different etymologies into account, I would say that the similar usage is entirely coincidental.

They appear to be pure coincidence. Similar to the fact that Thomas Crapper is known for his inventions related to the toilet. Taking a crap has nothing to do with Crapper's name. Although referring to a toilet as a crapper could be related to either (the word crap or then name Crapper).