The lockdown due to the COVID-19 pandemic has led to various sudden changes in a large number of individuals. In response, the question of how individuals from different social and economic strata cope with those changes has arisen, as well as how much they have affected their mental well-being. Choosing strategies that cope with both the pandemic and the well-being of the population has also been a challenge for different governments. While a large number of studies have investigated the mental health of people from different populations during the COVID-19 pandemic, few have explored the number and type of changes experienced during lockdown by the general population, alongside their relationships with health-related quality of life (HRQoL). To fill this research gap, an observational cross-sectional study on those associations was conducted in the French-speaking part of the Swiss general population. Data were collected from 431 participants during the first four weeks of lockdown due to COVID-19. Multivariate regressions were used to identify the sociodemographic profile of the population that experienced different types and numbers of changes during this period, the association of those changes with the HRQoL—mental and physical—and infection beliefs, and the perception of the governmental measures. We show that the more changes people experienced, the lower their mental HRQoL; however, adherence to governmental measures has helped people to cope with the imposed changes, even though the number of unexpected and unwished changes have strained their mental HRQoL. The low-income population experienced financial difficulties and changes in their food intake more frequently, while dual-citizenship or non-Swiss individuals declared conflictual situations more frequently. Sport practice had a positive association with mental HRQoL; nevertheless, a decrease in sport practice was frequently reported, which correlated with a lower mental HRQoL. Risk perception of COVID-19 increased with lower physical HRQoL score, which supports the efficiency of governmental communication regarding the pandemic. Our results support that government measures should be accompanied by effective and targeted communication about the risk of infection, in order to encourage all strata of the general population to follow such measures and adapt to the changes without unduly affecting their mental health. The usage of such tools might help to reduce the impact of policy-imposed changes on the mental HRQoL of the general population, by inducing voluntary changes in informed and engaged populations.