Learn French: Le blé ayant mûri, la moisson commence. - The wheat having ripened, the harvest begins.

This is an "absolute participle clause." It is a compact, elegant way to express cause or time. The key rule for this structure is that the participle must have its own subject (le blé) which is different from the main subject of the sentence (la moisson).

Why is it ayant mûri (having ripened) rather than just mûrissant (ripening)?

We use the perfect participle (ayant + past participle) to show that the ripening was completely finished before the harvest started. If you used the present participle (mûrissant), it would mean the harvest was beginning while the wheat was still in the process of ripening.

If the subject of the participle was feminine, would mûri need an extra -e at the end?

No. Because the verb mûrir uses the helping verb avoir (seen here as ayant), standard agreement rules apply. The past participle only agrees with a preceding direct object, never with the subject. If the verb had required être (for example, La nuit étant tombée), then it would agree with its subject.

Would a French speaker actually say this in everyday conversation?