Which well-known English Bible translations are based on the Vulgate? Which are not?
Knowledge about other languages (e.g. French) is welcome too.
A translation coming from an already translated work is called a "daughter translation." For example, the Septuagint in English is a daughter translation as it is based on the Septuagint instead of the Hebrew.
English Translations that use the Vulgate
Using the Vulgate as the basis for an English Bible has been done several times.
Modern Translations that Do Not Use the Vulgate
Most modern translations will examine the Vulgate to see
The first helps in cases where the Greek or Hebrew phrase appears only a few times. How other ancient translators understood the idiom can shed light on how it should be translated into English.
The second is used when the Greek or Hebrew manuscripts show differences. Looking at how other translations rendered a phrase helps determine if the phrase was original. For example, the Septuagint version of Numbers is very close to the Hebrew for most of the book (extremely close). Being so close most of the time, anytime it differs is evidence that the Hebrew manuscript used by the Septuagint translators differed from the tradition that survived to the present.
Most translations not in the list above will use the Vulgate for these purposes. For example, the New International Version relies on the original languages (which would be Greek, Hebrew, and Aramaic). New English Translation, The New American Standard Bible, and New Revised Standard Bible also use the Vulgate only for text critical issues.
The Douay–Rheims Bible is a translation of the Bible from the Latin Vulgate into English made in France for the Roman Catholic Church. Various editions are freely available online in numerous places. However, many later editions are based on more on the text of King James Version than on the Vulgate. You would want to try to find an earlier edition to remain closer to the Vulgate, but this will also mean that the translation will contain difficult (read old) English. Some attempts to modernize the language while remaining faithful to the Vulgate have been made.
Jacques Lefèvre d'Étaples translated the Vulgate into French in 1530 (which was also the first complete Christian bible available in the French language). I cannot find it online - I am only finding the later 1564 Geneve bible which was based on Calvin's translation from the Greek and Hebrew texts.