  We present a moduli dependent target space effective field theory action for
(truncated) heterotic string toroidal compactifications. When moving
continuously along moduli space, the stringy gauge symmetry
enhancement-breaking effects, which occur at particular points of moduli space,
are reproduced. Besides the expected fields, originated in the ten dimensional
low energy effective theory, a new vector and scalar fields are included. These
fields depend on "double periodic coordinates" as usually introduced in Double
Field Theory. Their mode expansion encodes information about string states,
carrying winding and KK momenta, associated to gauge symmetry enhancements.
Interestingly enough, it is found that a non-commutative product, which
introduces an intrinsic non-commutativity on the compact target space, is
required in order to make contact with string theory amplitude results.
