While APB unjustifiably lept to a conclusion and you’re quite in order to call him on that, the above is itself inaccuate information. Either Greene (who I freely admit I haven’t read) or yourself is garbling the citation.
The only work in the British Library catalogue (you can reach it online from here) that this could be is by the Renaissance astrologer Lucas Gauricus, aka Luca Gaurico (1476-1558; Augustus Morgan describes him as the “astrologer of astrologers”). The entry is essentially as follows:
Tomus I.(-III.) Operum omnium… L.G. , etc. [Edited by Joannes Henricus Paedionaeus]
3 tom. Basileae, 1575. fol.
And, if anybody cares, the shelfmark is C.80.b.1. Your citation thus manages to get the author’s name, the title and the date of the work wrong. Without having seen it, I’d also expect that it’s actually better described as a posthumous compilation of all his writings.
At this point the issue gets murky. Turning to James Randi’s The Mask of Nostradamus (1990; Prometheus, 1993, p171-2), he discusses Gaurico’s prediction, but his details are significantly different. Based on an account in a 1835 book Archives Curieuses de la France (which he gives no further details of - boo, hiss), his version has a member of Henri II’s court, Claude l’Aubespine, claiming that on February 5th 1556 a letter from Gaurico arrived in Paris warning
So here the prediction dates from 1556, not Greene’s 1557, and it’s his 41st year, not his 42nd. Plus various other divergences. Randi then goes on to argue that in 1552 Gaurico had already predicted that Henri would “arrive at a vigorous and happy old age before he dies.” His citation for this prediction is also shoddy, but he’s evidently seen a Latin text (he thanks someone for the translation) and I’d guess it might be the:
1552 - Henricus Francorum Rex Christianissimus. Caterina Uxor Henrici Regis Francorum in Tractatus Astrologicus in quo agitur de praeteritis multorum hominum accidentibus per proprias eorum genituras ad unguem examinatus , Venise , C. TROJAN NAVO , BN :V 8783 , Col Univ
listed under Gauricus at this site.
Frankly, I have no idea whether either Greene or Randi has their text and dates accurate. Clearly at least one of them is using “credulously repeated information that was not available to [them] from an [original] historical source.” It wouldn’t surprise me if both versions are filtered through multiple intermediates. Forced to guess, Randi’s version personally seems to me more circumstantial and plausible. If nothing else, if Henri’s dates are "d.o.b.: March 31, 1519, 10:28 am, St. Germain-en-Laye. Date of injury: June 30, 1559, date of death: July 10, 1559 " then Henri died aged 40. A prediction of him dying in his 42nd year would just be wrong.