Introduction: The prognosis for late preterm and early term births (35–36 weeks’ gestation and 37–38 weeks’ gestation, respectively) remains unclear during the first year of life. Materials and Methods: The 2011 national PMSI (Program for the Medicalization of Information Systems) database was used to assess the 1-year prognosis of singleton children born alive, without congenital anomalies, and with a gestational age between 35 and 41 completed weeks of gestation. Three study groups were defined: late preterm (35–36 weeks’ gestation), early term (37–38 weeks’ gestation), and control group (39–41 weeks’ gestation). Results: Among the 681,961 children included, hospitalization between Day 0 and Day 27 (6.4% at 39–41 weeks’ gestation) was more frequent as gestational age decreased, including at 38 weeks’ gestation (8.8%). The same significant trend was observed for admission to the neonatal intensive care unit (5.8% at 35 weeks; 2.6% at 36 weeks; 1.0% at 37 weeks; 0.4% at 38 weeks; 0.3% at 39–41 weeks). Hospitalization between Day 28 and Day 365 occurred in 11.9% of the population (bronchiolitis: 17.1%; gastroenteritis: 10.6%; ENT conditions: 5.5%; accidents: 6.2%). The following were recorded: 277 in-hospital deaths from day 0 to day 27 [0.4/1,000], and 226 from day 28 to day 365 [0.3/1,000]. After adjusting for sex and gestational pathologies, the relative risks (RRs) of mortality remained significantly higher than 1 at 35, 36, and 37 weeks’ gestation. Conclusion: the prognosis for births between 35 and 38 weeks’ gestation is less favorable than at 39–41 weeks’ gestation.