Learn French: Ils habitent dans un village coquet. - They live in a charming village.

Because village is a masculine noun (un village). The adjective coquet (charming) is therefore in its standard masculine form. If we were talking about a feminine noun, like a house (une maison), you would use the feminine rule from this lesson: double the final consonant and add an 'e' to make it une maison coquette.

Do you pronounce the 't' at the end of coquet?

No, the final 't' in the masculine form coquet is silent (it rhymes with 'café'). However, if you were to use the feminine form coquette, the double 't' followed by an 'e' means the 't' sound is clearly pronounced.

I thought 'coquette' was a word for a flirtatious person. How can a village be coquet?

You are right that for people, coquet (masculine) or coquette (feminine) usually describes someone who is stylish, very careful about their appearance, or flirtatious. But when describing a place, a building, or a room, it simply means 'charming', 'pretty', or 'picturesque'.

Why does coquet come after village instead of before it?