Yes, the equivalent is tu. A few centuries ago, English had the same distinction as French: thou when addressing people at a certain level of familiarity, you in a formal or upper-class setting. In English, you became completely generalized and displaced thou (except when talking to God). In French, the normal singular form remains in use. In some dialects (essentially, in France and in Switzerland), the syntactic plural vous may be used with a singular meaning, when speaking to a single person in formal situations. The limit between tutoiement (when to use tu) and vouvoiement (when to use vous) can be very difficult to grasp, it is a major difficulty for non-natives and is even occasionally awkward for natives.

If you’re looking to convey the same archaic meaning as “thou” with a personal pronoun in French, there is no equivalent.

Of course, the direct translation of “thou” is “tu” and although it does completely translate the meaning of “thou”, it does not have any of the archaic connotations.

When thou was used as a colloquial singular second person

It was then used almost exactly as tu was at the same time in France, so you just have to map thou to tu and you to vous.

When thou is used as an overly formal archaism

I tend to follow the convention used by the translators of David Eddings’ Belgariad: to add French-like tutoiement and vouvoiement with respect to the familiarity between the characters, and to use pronouns with a capital first letter for thou, thee, thine…:

Mets toute Ta force d’âme à supporter Ton mal, ô aimable jouvenceau, l’exhorta jovialement Mandorallen […]
La reine des sortilèges, translation by Dominique Haas

It was perhaps inspired from the classical pronouns referring to God in some French bibles or other religion-related work Il, Tu, Son… which translate to thou and such in King James’ Bible.