Achieving high vaccination coverage among healthcare workers against seasonal influenza is a public health goal, particularly in the context of the COVID-19 pandemic. A questionnaire for healthcare workers practicing in France was posted online and distributed by the Geres network during the summer of 2020. The questions focused on their previous influenza vaccination status and the reasons for getting vaccinated or not, as well as their vaccination intentions for the 2020–2021 winter season and against COVID-19. A total of 3,556 healthcare professionals, most of whom work in healthcare, social, or medical-social facilities, responded. The results reflect, for both vaccinations, a professional gradient in vaccination uptake, which is higher among physicians than among nurses and lower among nursing assistants. The analysis reveals that it would be possible to improve influenza vaccination coverage by targeting staff who have been vaccinated only occasionally in recent years and by improving access to vaccination. Theoretical acceptance of COVID-19 vaccination appears to be correlated with influenza vaccination, even when administered sporadically.