Pronouncing Latin, Aramaic, Ancient Greek

How do people know how to pronounce dead languages? Are there rules?
Does a French speaker’s spoken Latin resemble an English speaker’s?

I’m assuming there’s no possible way of knowing what is or isn’t a correct pronunciation, as everyone who ever spoke the tongue is dead, and there hasn’t, AFAIK, been an organized method of universal pronunciation before the 19th century.

The church has carried on speaking Latin to some degree, but has there been an appreciable level of consistency? As far as pronunciation, is my guess as good as theirs?

The short answer for Latin specifically is that we know a great deal about how languages derived from Latin were/are pronounced, and that allows scholars to make educated guesses about the parent tongue. We also have the benefit of the treatises “On the Latin Language” by Varro and “The Oratorical Instruction” by Quintilian; these works describe a few oddities of pronounciation (and some common mispronounciations) that also allow scholars to fairly accurately determine letter sounds. Finally, the details of Latin poetry provides some additional data; we know for example that Latin had words that were spelled alike, but apparently pronounced differently (e.g. levis, where the e changes sound depending on whether the word means “light” or “smooth”).

For older, Near-East languages (Such as ancient Egyptian), I believe the modern pronunciation is fairly artificial. Many of these languages didn’t bother to write down the vowels, so, for example, the hieroglyphs used to create the word for “Egypt” (K-M-T) are often pronounced “Kemet”, even though this was likely not how the original word sounded.

Other ways to determine pronunciation are to look at errors in the works of copyists. In the days before printing (or even carbon paper), the method used to produce multiple copies of a text was to lock up a bunch of clerks and have them write down what a reader dictated from an original text. When we have multiple copies of a work, (as with, but hardly limited to, Christian scriptures), we can look at passages that make no sense, compare them to the corresponding passages in different texts, and see whether the written text can be understood differently if spoken. (Think of Mondegreens.)

Then, there are passages in stories that are important indicators of pronunciation, such as the passages in Hebrew dealing with the word Shibboleth.

Poetry that is intended to rhyme (although much poetry does not rhyme) provides clues to the pronunciations of final sounds. Poetry that is alliterative provides clues to the initial sounds of words.

Aramaic is similar enough to Hebrew (a modern Hebrew speaker can generally understand written Aramaic, although it takes some work) that it’s pronounced the same way.

Of course Latin was spoken over a wide area over many centuries. What sort of accent you want? 100AD Roman? 300AD Frankish? Still, we can make educated guesses about pronunciation by looking at old poems and songs as well as looking at the word in modern languages and tracing back.

So scholars have even made guesses at PIE (Proto-Indo-European), the language that sparked off the whole IE group.

Latin as spoken in the Church is different from Latin as pronounced by the Latins and later the Romans, IIRC from my high school Latin classes.