During the last decade, public health research has emphasised the growing public disaffection with vaccination. This contemporary vaccine hesitation (VH) refers to a delay in acceptance or refusal of vaccines, as well as agreement despite doubt and reluctance. We investigated VH among French parents of young children, with an emphasis on two key features of VH: trust towards physicians and commitment to vaccination issues. We targeted two populations with contrasting socioeconomic profiles, using in‐depth interviews (n = 25). Most parents exhibited some kind of VH, with differentiated attitudes across vaccines, including acceptance despite enduring doubts, especially for vaccines already provided to older siblings (‘vaccine inertia’). Despite the rise of the Internet and social media, our participants still strongly relied on face‐to‐face interactions with peers and significant others. Most participants trusted their own physician but this was the result of a selection process: they had engaged resources to find a physician they could trust. Participants with contrasted socioeconomic profiles struggled with the same dilemmas, and they committed themselves to the same quest to find the ‘right’ physician. Nevertheless, parents with a higher socioeconomic status were able to engage more resources and use a wider repertoire of actions, and they also displayed greater health literacy.