The COVID-19 outbreak has generated significant uncertainty about the future, especially for young adults. Health and economic threats, as well as more diffuse concerns about the consequences of COVID-19, can trigger feelings of anxiety, leading individuals to adopt uncertainty-reducing behaviours. We tested whether anxiety was associated with an increase in willingness to be exposed to the risk of COVID-19 infection (WiRE) using an online survey administered to 3,110 French individuals aged between 18 and 35 years old during the first pandemic wave and lockdown period (April 2020). Overall, 56.5% of the sample declared a positive WiRE. A one standard deviation increase in psychological state anxiety raised the WiRE by +3.9 pp (95% CI [+1.6, 6.2]). Unemployment was associated with a higher WiRE (+8.2 percentage points (pp); 95% CI [+0.9, 15.4]). One standard deviation increases in perceived hospitalisation risk and in income (+1160€) were associated with a -4.1 pp (95% CI [-6.2, 2.1]) decrease in the WiRE and +2.7 pp increase (95% CI [+1.1, 4.4]), respectively. Overall, our results suggest that both psychological anxiety and the prospect of economic losses can undermine young adults' adherence to physical distancing recommendations. Public policies targeting young adults must consider both their economic situation and their mental health, and they must use uncertainty-reducing communication strategies.