Learn French: Ils viennent d'acheter un bel édifice prestigieux. - They have just bought a beautiful prestigious building.

Because édifice is a masculine singular noun that starts with a vowel. To avoid the clashing vowel sounds of beau édifice, French uses the special mutated form bel to make the pronunciation smoother.

Does using bel mean that édifice is a feminine noun?

No, édifice is masculine, which is why we also use un and the masculine adjective prestigieux. The feminine form for "beautiful" is belle. bel is specifically a masculine form used only before vowels and mute H's.

Why is one adjective before the noun (bel) and the other after (prestigieux)?

Most French adjectives go after the noun, like prestigieux. However, a small group of short, common adjectives describing Beauty, Age, Number, Goodness, and Size (often remembered by the acronym BANGS) go before the noun. beau falls under the Beauty category.

Why does viennent d'acheter translate to "have just bought"?

The structure venir de combined with an infinitive verb (in this case, acheter) is the standard French construction used to express the recent past, meaning "to have just done" something.