Objectives During the coronavirus disease 2019 (COVID-19) pandemic, public debates overtly addressed the promises of new innovative drugs. Many of these debates pitted those who advocated for the development of new drugs by pharmaceutical companies against those who favored the repositioning of existing drugs. Our study explored perceptions of the association between drug novelty and effectiveness as well as perceptions of the role of the pharmaceutical industry in drug development. Methods Data were collected in January 2021 from a quota sample of the French population aged 18–75 years ( n = 1,000) during the second round of the “Health Literacy Survey 2019” (HLS19). Results We tested the hypothesis that individuals with a high level of familiarity with the health care system and those with a high level of trust in institutions are more likely to agree that new drugs are more effective than old ones and that drug development should be driven by the pharmaceutical industry. A quarter (25%) of respondents agreed that new drugs are always more effective than old ones. Agreement with this statement was stronger among respondents with a high level of familiarity with the health care system (as measured by the navigational health literacy score, OR 3.34 [2.13–5.24]). Respondents with a low level of trust in pharmaceutical companies or politicians were two times less likely to agree that new drugs are always more effective than old ones (OR 0.63 [0.42–0.95] and OR 0.68 [0.49–0.94], respectively). A high level of trust in pharmaceutical companies was reported by 42% of respondents, and 43% agreed that drug development should be driven by the pharmaceutical industry. Conclusion Our study shows that the perceived effectiveness of innovative drugs is associated with familiarity with the health care system and trust in institutions.