Auxins are a class of organic substances known as plant-growth regulators, which act on plant physiology, promoting its full development. However, due to the great instability of these substances among the diversity of crops and cultivation environments, it is necessary to seek more efficient modes of application, which lead to a homogeneous distribution and promote a sustained release according to the plants demand. Seed coating, using films containing a biodegradable polymer and auxins intercalated into layered compounds, emerges as a very promising approach to a new form of growth regulator application. Thus, the presented work had three aims: (i) the synthesis and characterization of an organic–inorganic hybrid material containing a layered double hydroxide (LDH) of zinc and aluminum and the synthetic auxin 1-naphthalenoacetic acid (ZnAl-NAA-LDH), (ii) the coating of bean seeds (Phaseolus vulgaris L.) with composite films produced from mixtures of alginate polymer and ZnAl-NAA-LDH, and (iii) the evaluation of the plant response by bioassays. The hybrid ZnAl-NAA-LDH was characterized by a set of analytical techniques, including powder X-ray diffraction, thermogravimetric analysis coupled to differential scanning calorimetry and mass spectrometry, specific surface area measurement, and scanning electron microscopy. Bioassays were performed with the seeds coated with the composite film to assess the germination rate and germination speed index of the seeds, as well as biometric analyses including measurements of root area, root fresh matter, and shoot length of the plants. The bioassay performed in soil pots showed that the alginate film containing ZnAl-NAA-LDH yields an enhancement regarding root area, fresh root matter and shoot length of plants. Thus, films produced from a mixture of alginate and the hybrid material containing the growth regulator intercalated into LDH can be a viable alternative to enhance plant development, which can be included in seed management.