Learn French: Le troupeau émergeant de la forêt est calme. - The herd emerging from the forest is calm.

Here, émergeant is a present participle expressing an action, not a verbal adjective expressing a state or quality. We know it is acting as a verb because it has a complement attached to it (de la forêt). The present participle of verbs ending in -ger keeps the e before the a to maintain the soft "g" sound. The verbal adjective form is émergent, which is used like a regular adjective (as in les pays émergents meaning the emerging countries).

If the sentence was about plural cows instead of a singular herd, would émergeant become plural?

No, it would still be spelled émergeant. Because it is acting as a present participle and not a verbal adjective, it is strictly invariable. It never changes to match the gender or number of the noun. You would write: Les vaches émergeant de la forêt sont calmes.

Could I say qui émerge instead of émergeant?

Yes! In French, the present participle is often used in written or formal language to replace a relative clause starting with qui. Saying Le troupeau qui émerge de la forêt est calme is perfectly correct and is actually much more common in everyday spoken French.

Why does forêt have a circumflex accent?