Because the phrase was likely in oral circulation long before Crèvecoeur wrote it down, the "true" origin is a matter of interpretation.
He described it as a period of hazy, smoky calm after a frost, noting that Native Americans used this time to hunt game after the leaves had fallen. This supports the as the earliest recorded explanation.
Âïåðâûå íà íàøåì ñàéòå?
Çàðåãèñòðèðóéòåñü, ÷òîáû çàâåñòè ñâîé ëè÷íûé êàáèíåò. indian summer etymology
Ðåãèñòðàöèÿ