What is the difference between "park" and "parc"?

Solution 1:

English got the word park from French parc and in Middle English it was spelled as both park and parc. Then English spelling standardized to only use park.

After spelling was standardized, oyster park/oyster parc, was imported from the French parc à huîtres/parc aux huîtres. So sometimes this very specific use of the word is spelled with a c.

The OED marks stand-alone park/parc in the oyster sense as obsolete.

The Guardian has an example of the c spelling:

We put-putted out to a buoy marking his underwater oyster parc, a fenced-off section of the bay bottom, and we sat . . . and sat . . . and sat, in the roaring August sun, waiting for the tide to go out.

In essence, except for oyster parc, park is always spelled with a k in English.