Abstract Background Parents of term and preterm infants hospitalised at birth experience a stressful situation. They are considered as primary caregivers in neonatal units and are encouraged to participate in their child’s care. Objectives The aim of our study was to analyse the feelings of parents participating for the first time in caregiving for their baby admitted at birth in a neonatal unit in France and to compare the feelings reported by parents of term and preterm infants. Methods An online survey was created in 2014 for parents who had a baby hospitalised at birth. We analysed parents’ responses to this open‐ended question: “How did you feel when you participated in caregiving for your baby for the first time?” using a qualitative discourse analysis by two analysts. Themes were identified and coded. Results Between February 2014 and March 2018, 1603 parents of preterm infants and 239 parents of term infants responded to this open‐ended question. Twenty‐five per cent of parents expressed positive feelings exclusively (confidence, ease, joy, pride, feeling supported by healthcare professionals, by their family and feeling of being a parent), 41% expressed negative feelings exclusively (stress, fear, feeling of being judged, frustration, anger, uselessness and clumsiness) and 34% expressed mixed feelings (both positive and negative). Parents of term infants expressed less frequent feelings of stress and fear than parents of preterm infants: with a relative risk (RR) of 0.69, 95% confidence interval (CI) 0.56, 0.87. Parents of term babies more frequently expressed feelings of frustration: RR 2.40 (95% CI 1.33, 4.32). Conclusions Infant‐ and Family‐Centred Developmental Care supportive programmes are recommended within neonatal units in order to improve the experience of parents participating in caregiving for their baby hospitalised at birth.