Others have suggested many ways to express falling in love in Latin.
Let me address the grammar of your suggestion, even though it was too literal as a translation.
There is only one problem, but it occurs twice.
Pay attention to which case is needed with each preposition:
Cum requires the ablative.
Both haec and lingua need to be in this case: hac lingua.
A less literal (but perhaps more idiomatic) proposal:
Amore huius linguae accendor
(“I am ablaze with love for this language!”).
Or, slightly less hot perhaps:
Studium eius linguae me excitat
(“The interest for [love of] this language excites me,”
i.e. “I am very much interested in, I love this language”).
Although the inchoative suffix -sc- is productive, I would advise against using it in everyday speech unless the verb is already a common one. I could say "pugnasco" (unattested) or "puellasco" (a couple usages), but it would call attention to itself in a way that doesn't seem fitting for the phrase "falling in love." Since I ...
Oxford [English-to-Latin section (under "fall")], offers "adamo" = "to fall in love with", taking the accusative case. (In the Latin-to-English the definition of "adamo" is "to love passionately". I am always suspicious when the two sections fail to coincide.)
Lewis & Short gives "to love truly, ...
Latin has an inchoative suffix -sc- which indicates that a certain state is beginning, and which is quite productive (rubesco, senesco, reconvalesco, ...). And indeed, there is the verb amasco – "to begin to love", so that you could say
hanc linguam amasco
Sebastian is right. It's repeated in order to resume the sentence after a lengthy clause. We see this even in Classical Latin. I hesitate to call it a mistake, since it is so often deliberately chosen in order to alert the reader that the sentence has resumed.
From Wills, Repetition in Latin Poetry, p. 66:
Cicero also uses gemination to resume unfinished ...