A word that describes someone who is obsessed with the concept of love

It can't be "romanticist" since the definition as given by the SOED is

"an exponent or admirer of romanticism in literature, art, or music".

There is the verb "to romanticize", though, with the following meanings (SOED).

1 v.t. make romantic or unrealistic in character; describe or portray in a romantic fashion
2 v.i. Indulge in romantic thoughts, words or actions

There is then the noun which corresponds to the verb: "romanticization" and also the noun "romanticizer", the definition of which is found in the Wiktionary with the following definition.

One who romanticizes

From the meaning of the verb then, a romanticizer can be someone who gives a turn to certain situations so that they appear more romantic than they really are, and someone such as that might be a writer or a film director or simply someone with an opportunity of some sort to shape his/her own environment and life. That however does not make of this person necessarily someone who is obsessed with the romantic aspect of life. Otherwise, it might be someone that goes after what appears romantic, who indulges in it.

To describe the particular sort of romanticizer that romanticizes everything obsessively I'd use a phrase like romanticizer to excess.