Fermat's opponents

Maybe the following article http://arxiv.org/abs/1306.5973 (Is mathematical history written by the victors?) and references therein will be useful :-).

Fermat's life and work is carefully investigated in the book "The Mathematical Career of Pierre de Fermat, 1601-1665" by Michael Sean Mahoney: http://press.princeton.edu/titles/5449.html See, however, Gerry Myerson's comment below and https://mathematicswithoutapologies.wordpress.com/2015/03/25/andre-weil-vs-history-of-mathematics/

P.S. I have just found two papers by Klaus Barner (in French) which might be useful (in case you are not already aware of them):

https://eudml.org/doc/10129 (Pierre Fermat Sa vie privée et professionnelle)

http://www.zeitschrift-rechtsgeschichte.de/de/article_id/581 (Fermat et l'affaire Delpoy)

P.P.S. Two more papers by Klaus Barner:

http://www.degruyter.com/view/j/dmvm.2001.9.issue-3/dmvm-2001-0070/dmvm-2001-0070.xml (Das Leben Fermats)

http://www.math-in-europe.eu/images/information_pdf/hist_phil_pdf/hist_pdf/barner.pdf (Pierre de Fermat (1601? - 1665) His life beside mathematics)

Russian science fiction writer Alexander Kazantsev wrote a historical novel about Fermat's life: http://www.litmir.me/bd/?b=261604 (Острее шпаги). A German translation of it does exist: https://www.amazon.de/Alexander-Kasanzew-Sch%C3%A4rfer-als-Degen/dp/3355003638 (Schärfer als Degen).

From the more scientific point of view, maybe the following book will be useful: https://www.amazon.co.uk/Public-Life-Toulouse-1463-1789-Cosmopolitan/dp/0801421918 (Public Life in Toulouse, 1463-1789: From Municipal Republic to Cosmopolitan City, by R.~A.~Schneider).

The point (5) is at most doubtful. It was made by Mahoney in his book on Fermat, but Mahoney's interpretation of what Digby writes to Wallis does not correspond to what Digby actually writes, as quoted by Weil in his review cited in comments:

I have had nothing from him [Fermat] but excuses . . . . It is true it came to him upon the nick of his removing his seat of Judicature from Castres to Tholose; where he is supreme Judge in the soveraign Court of Parliament. And since that, he hath been taken up with some Capital causes of great importance; in which in the end he hath given a famous and much applauded sentence for the burning of a Priest that had abused his function; which is but newly finished; and execution done accordingly. But this which might be an excuse to many other, is none to Mons. Fermat, who is incredibly quick and smart in any thing he taketh in hand.

So Fermat did not answer with his usual celerity to mathematical questions, but there is nothing but Mahoney's imagination that indicates that it was because he was shocked by a judicial decision.

The point (3) might be valid, but remember that Descartes had much more serious problems with (ecclesiastic and otherwise) authorities than Fermat ever had (if indeed he had any), so it seems unlikely that his "ennemies" would use Descartes against him.

(1), (2) and (4) are unrelated to the mathematical work of Fermat.

Given the evidence provided, I don't see any reason to think hat Fermat was afraid of being found heretical for some part of his mathemamatical work.

I understand you are asking for more evidence concerning this supposition, which I have not, pointing in one direction or te other, but that supposition seems to me rather arbitrary at this point.