I'll leave the later period, toward the Reformation, for another expert (that's u/sungainstgold's specialty, I believe), but yeah, earlier in the Middle Ages, there was a fear that some random person reading the Bible would lead to misinterpretations. The Church didn't totally restrict the Bible and it wasn't entirely forbidden to translate it - the church wasn't trying to keep people uneducated and ignorant, as the conspiracy theory often goes. But there were fairly limited circumstances where laypeople could read a vernacular Bible.

First of all, medieval people were generally aware that the Latin Bible was itself a translation, since it was originally in Greek and Hebrew. So the church wasn’t against reading translations specifically, it was just that the version used by the Catholic Church in Western Europe was the Latin “Vulgate” translated by St. Jerome in the 4th century. Other places used their own Bibles, in Greek or Arabic or Armenian or Aramaic. So, why didn’t the Catholic Church have Bibles in the other common languages of Europe (English, German, French etc.)?

It was partly because vernacular languages were not really seen as “real” languages like Latin. French or Italian were considered to be just a debased form of Latin. Why would anyone want to read any literature in those languages, much less the Bible? Of course there were Germanic and Slavic languages and other languages that weren’t descended from Latin, but for Catholic Europe, the language of learning, education, diplomacy, science, and every other field was Latin. Educated people from Portugal to Poland learned to read Latin in school, not their local vernacular. The Bible was in Latin because anyone who could read was already reading in Latin.

Preachers preached in the vernacular, there were Passion plays and morality plays and other dramatizations of Biblical stories in vernacular languages, and people could learn about the Bible from art and architecture. And there were lots of “glossed” Bibles, i.e. Latin Bibles with vernacular translations or notes in the margins or between the lines, in English, Irish, French, German, etc...clearly people wanted to know what the Latin meant, even educated people.

What the Church was opposed to was people making an unauthorized translation that might introduce errors, and in extreme cases might be heretical. The Bible, in the Church's eyes, is difficult to understand and interpret and it took years of studying to comprehend it properly. Vernacular translations were allowed, but only if they were properly supervised by the Church. For example there were French translations like the “Bible d’Acre”, and French paraphrases with historical notes and commentaries like the “Bible Historiale” or the “Bible Moralisée”.

So, the Church wanted everyone to have access to the Bible, through preaching and even through reading it, as long as it's done by a Church-educated expert who isn't gong to accidentally introduce some kind of bizarre heresy because they don't understand what they're reading.

Some further reading:

- Peter Biller and Anne Hudson, eds, Heresy and Literacy, 1000-1530 (Cambridge University Press, 1994)

- Katherine Walsh and Diana Wood, The Bible in the Medieval World: Essays in Memory of Beryl Smalley (Blackwell, 1985) - especially Leonard E. Boyle’s article "Innocent III and vernacular versions of Scripture"

- Rosemarie Potz McGerr, (1983). “Guyart Desmoulins, the vernacular master of histories, and his Bible Historiale” (Viator 14, 1983)

- Pierre Nobel, “Early Biblical Translators and their Readers: the Example of the Bible d'Acre and the Bible Anglo-Normande’’ (Revue de linguistique romane 66, 2002)