What Did the "Geneva Reformers" Have Against Exodus 2:22?

What I believe is being referred to is that the Douay Rheims says "And she bore him a son, whom he called Gersam, saying: I have been a stranger in a foreign country. And she bore another, whom he called Eliezer, saying: For the God of my father, my helper hath delivered me out of the hand of Pharao." The Geneva Bible says "And she bare a son, whose name he called Gershom: for he said, I have been a stranger in a strange land." The verse is not completely missing, but the Geneva Bible is missing the second sentence (most modern Bible translations lack it as well).

The reason for this is that the Douay Rheims is translated from the Latin Vulgate, whereas the Geneva Bible's Old Testament (and that of most modern translations) are translated from the Hebrew Masoretic Text.

Francis de Sales here appears to be criticizing the usage of the Masoretic Text on the grounds he believes that the Vulgate's reading, at least in this verse, to be correct. While the Masoretic Text is in the original language while the Latin Vulgate is a translation, something in the favor of the Vulgate is that the Masoretic Text was compiled in the latter portion of the first millennium AD by the Masoretes (the Old Testament obviously preceded them, it's just they were the ones who produced the specific Masoretic Text) and our earliest full manuscript of it comes from around 1008 AD. We don't know exactly what Hebrew manuscripts were used to translate the Latin Vulgate, but they would have been ones from the fifth century at the latest, thus giving an attestation to earlier manuscripts even if it is a translation.

What Francis de Sales seems to be arguing is that the reading in the Masoretic Text is wrong, referring to "the Septuagint and other translations" which include the Eliezer reference.

In regards to the Septuagint (a Greek translation of the Old Testament done around the third or second century BC, also known as LXX), it seems to me that some manuscripts have the "full" version, but not all. Therefore, some Septuagint translations omit it (see Exodus NETS and Exodus LXX) but an interlinear at Interlinear Greek English Septuagint Old Testament (LXX) includes it. It appears in some manuscripts but not others is mentioned in the Keil and Delitzsch Biblical Commentary on the Old Testament (available with other commentaries at BibleHub's Exodus 2:22) which says:

(Note: In the Vulgate the account of his birth and name is interpolated here, and so also in some of the later codices of the lxx. But in the oldest and best of the Greek codices it is wanting here, so that there is no ground for the supposition that it has fallen out of the Hebrew text.)

Admittedly, the Keil and Delitzsch Biblical Commentary was done in the 19th century and therefore its assessment concerning what the best Greek codices are may have been subsequently revised, but the point is it affirms that it is found in some but not all Septuagint manuscripts.

Francis de Sales does refer to "other translations", but I am not sure what he is referring to here--the Vulgate is obviously one, but he uses the plural which indicates there are more. At this point we're going a bit beyond my knowledge, so I cannot comment on what other translations may have had the Eliezer mention.

I checked into the Dead Sea Scrolls to see if they might help settle the question, as they go to the BC era. "The Dead Sea Scrolls Bible" is a great resource for looking up specific verses to see if they were found in the Dead Sea Scrolls and if they vary from the Masoretic Text (the Dead Sea Scrolls match up strongly with the Masoretic Text, but there are a few points of divergence, sometimes interestingly favoring the Septuagint). Unfortunately, while there was a scroll that included this section of Exodus, it was very fragmented and I do not think we have enough to know whether it includes the extra text or not.

So, the short version is that what seems to be happening is Francis de Sales is saying Protestants were wrong to follow the Masoretic Text in this case and omit the Eliezer portion, appealing to the Latin Vulgate and Septuagint as evidence that it was in the original Hebrew, even if it did not make it into the later Masoretic Text. I do not have enough information to try to ascertain as to which reading is better considered the original and weigh in on whether he was right or wrong, but that is my impression.