From the given context, I think it can be safely said that that the guy (perhaps jokingly) suspected the woman was one of the following:
- A beast disguised as a human using a shape-shifting ability.
- A person possessed by a beast.
- A 獣人 (beast-human hybrid) who has a tail by nature. Many fictional 獣人 are visually identical to human beings except for the ears and the tail (e.g., Kemono Friends).
There are countless fictions and folktales related to this topic in Japan (and also in the world), and I don't know which is the intention of the guy. It all depends on the settings of the movie and the scene. Japanese mysterious foxes are strongly associated with shinto shrines, so if the guy picked up the woman near a shrine, it may be reasonable to assume this is a reference to a fox.
Even if your scene is related to a fox, "kitsune-tsuki" may not be relevant. A Japanese fox is reputed to have the ability to both shape-shift to a human and possess a human, and the term "kitsune-tsuki" refers only to the latter. In addition, in many fictions, a shape-shifted beast tends to have a tail whereas a person possessed by a beast tends not to have a tail.