Background: The impact of the new chemotherapy, fluorouracil plus leucovorin, oxaliplatin, and docetaxel (FLOT) on body composition in gastric cancer (GC) patients remains unknown. We assessed body composition changes of GC patients receiving the FLOT regimen and their impact on treatment outcomes. Methods: Preoperative pre- and post-FLOT computed tomography (CT) scans of advanced GC patients were studied. Lumbar skeletal muscle index (SMI) and adipose indices were calculated before and after FLOT. Results: A total of 26 patients were identified between April 2019 and January 2020. Nineteen patients were sarcopenic at diagnosis. The mean BMI decreased (from 24.4 ± 3.7 to 22.6 ± 3.1; p < 0.0001) as well as the SMI (from 48.74 ± 9.76 to 46.52 ± 9.98; p = 0.009) and visceral adipose index (VAI) (from 49.04 ± 31.06 to 41.99 ± 23.91; p = 0.004) during preoperative FLOT therapy. BMI, SMI, and VAI variations were not associated with toxicity, Response Evaluation Criteria in Solid Tumors (RECIST), response, delay and completion of perioperative FLOT chemotherapy, and the execution of gastrectomy; a decrease of SMI ≥ 5% was associated with a higher Mandard tumor regression grade (p = 0.01). Conclusions: Almost three-quarters (73.1%) of GC patients were sarcopenic at diagnosis. Preoperative FLOT was associated with a further reduction in SMI, BMI, and VAI. These changes were not associated with short-term outcomes.