Learn French: Il a beaucoup ronflé à cause de son rhume. - He snored a lot because of his cold.

In French compound tenses like the passé composé, short or common adverbs (like beaucoup, bien, déjà, and mal) go directly between the helper verb (a) and the past participle (ronflé). English often puts "a lot" at the end of the phrase, but French requires Il a beaucoup ronflé.

Why does this sentence use à cause de instead of parce que for "because"?

Parce que must be followed by a full clause with a subject and a verb (for example, parce qu'il était malade - "because he was sick"). À cause de translates to "because of" and is followed by a noun (son rhume). Note that à cause de is typically used when the cause is negative or undesirable!

I learned that "cold" is froid. Why is the word rhume used here?

Froid refers to the temperature (the weather being cold, or feeling physically cold). When you are talking about the minor viral illness where you cough and sneeze, the French word is the noun un rhume.

Why does it say son rhume? Does son agree with Il (He)?

No, French possessive adjectives agree with the noun that is owned, not the person who owns it. Because rhume is masculine singular, you must use son. Even if the sentence was about a woman snoring (Elle a beaucoup ronflé...), it would still be son rhume!