(1) Background: A substantial proportion of COVID-19 patients continue to experience long-lasting effects that hamper their quality of life. The objectives of this study were (1) to report the prevalence of persistent clinical symptoms 6–12 months after the onset of COVID-19 and (2) to identify potential factors at admission associated with the occurrence of long COVID. (2) Methods: A prospective study was conducted among COVID-19 adult patients, hospitalized in four French university hospitals. Patients were invited to two ambulatory follow-up medical visits, 6–8 months (visit #1) and one year (visit #2) after the onset of their COVID-19. A multivariate logistic regression was performed to assess factors associated with long COVID. (3) Results: In total, 189 patients participated in this study (mean age of 63.4 years). BMI > 30 kg/m2 (aOR 3.52), AST levels between 31 and 42 U/L (aOR 8.68), and AST levels > 42 U/L (aOR 3.69) were associated with persistent clinical symptoms at visit #1. Anosmia (aOR 13.34), AST levels between 31 and 42 U/L (aOR 10.27), stay in ICU (aOR 5.43), pain (aOR 4.31), and longer time before hospitalization (aOR 1.14) were significantly associated with persistent clinical symptoms at visit #2. Patients with ageusia (aOR 0.17) had a lower risk of long COVID. (4) Conclusions: This study showed that some patients experienced persistent clinical symptoms one year after COVID-19 onset that were associated with some determinants at the acute phase/stage.