How to say i started falling in love with it in french?

"J'ai commencé à tomber amoureux" is "I started to fall in love"

"Je commençais à tomber amoureux de [someone]" is "I started to fall in love with [someone]"

You use the passé composé because "Je commençais" is "I was starting to"

You do not say "je le commençais" or "Je l'ai commencé" because there is no direct object pronoun. "commencer" is followed by a verb so it has no object complement and "tomber amoureux de [someone]" has no object complement because the person is part of the adjectival group "amoureux de [someone]".

There is no direct object.

Of course, "amoureux" becomes "amoureuse" if the person falling in love is a woman.

Note that the expression "tomber en amour avec" (a calque of the English "to fall in love with") exists in Canada and works the same as "tomber amroureux de"