I continue to suspect that Bernier was not the English translator; he assembled these essays out of Gassendi's broader corpus, translating from Latin to French as he did so. And an anonymous translator (probably the author of the preface, who refers to both Gassendi and Bernier in the third person) translated Bernier's French into English. I can't find that Bernier ever wrote anything in English.
Edit; Unfortunately, this text does not appear in Halkett and Laing's Dictionary of the Anonymous and Pseudonymous Literature of Great Britain. It would have appeared alphabetically between these two entries.