The spear fishing laws are clearly stated on FWC Web site. 100 yards from bridges where fishing is permitted and 100 yards from a public swimming area.
As Phil Foster Park does not include any of the surrounding submerged land, Palm Beach County Parks Department seems to have no juristication. In fact, if you are legally engaged in spearfishing or collecting tropicals (also legal around the bridge) remember this:
Title XXVIII
NATURAL RESOURCES; CONSERVATION, RECLAMATION, AND USE
Chapter 379
FISH AND WILDLIFE CONSERVATION
View Entire Chapter
379.105 Harassment of hunters, trappers, or fishers.—
(1) A person may not intentionally, within a publicly or privately owned wildlife management or fish management area or on any state-owned water body:
(a) Interfere with or attempt to prevent the lawful taking of fish, game, or nongame animals by another.
(b) Attempt to disturb fish, game, or nongame animals or attempt to affect their behavior with the intent to prevent their lawful taking by another.
(2) Any person who violates this section commits a Level Two violation under s. 379.401.
History.—s. 2, ch. 90-170; s. 27, ch. 2006-304; s. 9, ch. 2008-247.
I'm not advocating any particular behavior, just pointing out the law.