I think the main flaw of Le Portrait de Petit Cossette is that it was trying to be like Evangelion. The problem with this is that there can only be one Evangelion, as evidenced by the fact that I’m using Eva as an example of what Petit Cossette tried to do. But that aside!
Petit Cossette is a sort of time-traveling contemporary occult horror story with a dash of romance (or more, depending on your definition of the word) thrown in. Eiri is an artist working in his uncle’s antique store when one day, while handling a Venetian glass, he begins to see visions of a young woman through it. As the visions increase, Eiri withdraws further and further from his friends, until one midnight the girl, Cossette, finally makes contact with him. As his friends grow more concerned about his heath and sanity, Cossette lures Eiri into a nasty world of revenge against her murderer–a man who, she claims, has been reborn in Eiri.
Le Portrait de Petit Cossette is a 3 episode OVA that came out in 2004. It was licensed by Sentai Filmworks, who released the English dub in that same year. There was also a 2 volume manga from 2004 that was translated by Tokyopop; but I haven’t read it, so I can’t say whether it’s similar or not!