While looking a little more at early modern texts that talk about sympathy, I came across this (which is apparently distinguished by being the earliest text returned in a search for ‘sympathy’ and its variants in Early English Books Online.)
Likewise néere to this Ilande is founde a kynde of fish, and also vpon the coaste of America very daungerous, also much feared and redoubted of the wilde men, for that she is a rauening fish, and as daungerous as a Lyon or a Woulfe famished: this fish is named Houperou, in their language, and eateth other fish in the water, excepting one that is as greate as a little Carpe the which foloweth him alwayes, as if there were some Sympathia or secrete loue betwene them, or else he foloweth him for to be preserued and kept sure from other fishes.
That comes from pp.117-8 of André Thevet’s The new found worlde, or Antarctike wherin is contained wonderful and strange things… (London, 1568), an English translation of his 1557 Les Singularitez de la France antarctique (EEBO-TCP record). The ‘Antarctike’ here is not the antarctic continent, but France Antarctique, a sixteenth-century French colony in Brazil.
There’s a short biography of Thevet on the English-language Wikipedia, and a rather longer one on the French-language WIkipedia, which also has an article on Les Singularitez de la France antarctique. One can also download scans of the French edition of the book from Gallica, and from a UVa site.