The Three Loves
The third (first, actually) wasn't storge, it was agape, which is the first mentioned in the list of Greek words in the original posting. Agape is the personal love with no expectation of return or reward, like the love of God for his creatures, humans for God, humans for other humans (without any erotic element, which would be eros.

I take it that the Greek list is in modern Greek, which I know nothing about. A list in koine Greek would include philein but not storge.

Besides the words listed in French, there is the phrase avoir envie de ....