I think the confusion comes in when we consider that "fool/fooling around" takes its rules from the type of clause we are using.
As you know, when a verb is the subject of a sentence, it is used in "-ing" form.
Fooling around is what he does.
The adding of "-ing" is also common practice for forming nouns from verbs.
When a verb is the subordinate clause of a sentence, we modify it accordingly (in this case an infinitive stem):
What he does is fool around.
So I feel like your two sentences are us applying the two rules above, but ordering our sentences differently. Your first example is like a list of "what he does":
He does more than just fool around, eat food and lift weights.
Whereas your second uses a verb masquerading as a noun:
He does more than just fooling around and playing football
So, in summary, I think both are correct, but the first sounds more natural to me, since you are listing "what he does" as subordinate clauses (He does play, he does lift weights), and sometimes, verbs employed as nouns can sound a little false/forced:
He does nothing but reading books
Sounds (and is) entirely incorrect, whereas
He does nothing but read books
Carries the agreement from "does".