Span is an older strong past tense form of spin — this is the past tense form that existed in the older Germanic ancestors of English. In German, for example, the past tense of spinnen is still spann. In English, span has mostly fallen out of use in favor of spun for both the past participle and simple past forms. This is a form of paradigm leveling. It has occurred in other words like sting (no stang) but not in ring (where we do have rang).
The OED actually gives your quote as follows:
When Adam dalve, and Eve span, Who was than a gentle~man?
Note that this quote is dated from 1560. At this time, span was a more common past tense form, and of course well-known quotes are usually more resistant to being updated to modern vocabulary and grammar. (Interestingly, it looks like dalve has been out of use long enough by now that, at least where you read it, it was updated to delved.)
The OED cites uses of span dating up to the late 19th century, for example, this quote from 1882:
In bad weather she sat at home and span.
So, your answer is: if this sentence were constructed today, then spun would be the correct word, as you suspect. This is simply an old quotation where that word remains fossilized.