Docetaxel, Cisplatin and Fluorouracil in Treating Patients With Previously Untreated Stage II-IV Nasal Cavity and Paranasal Sinus Cancer

Inclusion Criteria: * Patients must have a confirmed (by a MD Anderson Cancer Center \[MDACC\] pathologist) cytologic or histological diagnosis of locally advanced squamous cell carcinoma, poorly differentiated carcinoma, or sinonasal undifferentiated carcinoma of the nasal cavity and/or paranasal sinuses. * Stage II-IV disease; tumor (T) 2-4, node (N) any, metastasis (M) 0. Measurable disease is required with the following criteria: Measurable lesions can be accurately measured, with at least one diameter \>= 1.0 cm by spiral computed tomography (CT) scan or magnetic resonance imaging (MRI). Lesions can be bidimensionally measurable or unidimensionally measurable. Every effort should be made to measure lesions in two dimensions. Measurable disease is present if the patient has one or more measurable lesions. Non-measurable lesions/disease are all other lesions, including small lesions (those with measurements \< 2.0 cm; or \< 1.0 cm with spiral CT). * Eastern Cooperative Oncology Group (ECOG) Performance Status (PS) 0-1. * Absolute peripheral granulocyte count (AGC) of \>= 1500 cells/mm\^3. * Platelet count of \>= 100,000 cells/mm\^3. * Total bilirubin =\< upper limit of normal (ULN). If the patient has a history of Gilbert's Syndrome, check direct and indirect bilirubin. If in the judgment of the attending medical oncologist it is safe to treat the patient, the patient will be considered eligible for this criteria. * Alkaline phosphatase =\< 2 x ULN. If in the judgment of …