So, I didn't actually hate it.
Let me begin with a gif, though.
That's Drusilla, from Buffy the Vampire Slayer. And, sadly, that is what I pictured every single time I read the name of the main character. It was . . . distracting.
Now that I've gotten that out of my system, I shall talk about the book.
When I read a gothic romance, I expect two things. Gothic. Romance. This was a very low key romance - so low key, in fact, that I do not believe that the two romantic leads actually ever touched each other until the hero proclaimed his undying love for the heroine. There was basically no chemistry between them at all.
What does "gothic" really mean? To me, it absolutely requires a certain aesthetic that invokes gloom, dread and a sense of supernatural possibility and danger. I suppose that the titular India fan was supposed to offer that "gothic" feeling, but it really didn't work because sensible Drusilla just didn't buy it and so the reader didn't buy it, either. The other dangerous elements - specifically, Drusilla becoming embroiled in the Sepoy Mutiny of 1858, wasn't even remotely gothic.
As a piece of historical fiction, it rather reminded me of The Shadow of the Moon, by M. M. Kaye, which I quite enjoyed. Unfortunately, Holt simply does not write at the level of M. M. Kaye. I didn't find it to be awful, but there was nothing special about it.