What would the best word be to describe a frog-lover that ends with the -phile root?
The word for the fear of frogs is batrachophobia, although Wikipedia suggests it is ranidaphobia. However, the suffix -phile is Greek, and there is a "rule" that the components for such a word should all be from the same root language, rather than mixing root languages. (This is really more of a common style choice and not a grammatical requirement.) The Classical Greek word for frog is batrachos (and rana is Latin). So, following that logic, the Greek word for frog should be used (rather than Latin or anything else).
So, I think the purist answer for someone who loves frogs would be batrachophile.
The don't-care-about-mixing-Latin-and-Greek answer would be ranidaphile (with the advantage that this connects with ranidae, the scientific term for the most common frog family).
The who-cares-about-disguising-English-with-smart-sounding-words-from-dead-languages answer is frogophile.