English Verb Origins?

From my limited knowledge of French, "to"less infinitives are common.
I like to study.
J'aime etudier.

"J'aime a etudier." isn't right in French (right?), but it's what English does. Where did that use come from?

The "to" is considered a part of the word, as far as I remember. In etudier, the "er" is the same as "to"; when conjugated, the "to" is lost.

EDIT: I wasn't reading the question correctly. I think it's either Old English or Germanic...