During the unprecedented COVID-19 pandemic, social media has been extensively used to amplify the spread of information and to express personal health-related experiences regarding symptoms, including anosmia and ageusia, 2 symptoms that have been reported later than other symptoms. Objective Our objective is to investigate to what extent Twitter users reported anosmia and ageusia symptoms in their tweets and if they connected them to COVID-19, to evaluate whether these symptoms could have been identified as COVID-19 symptoms earlier using Twitter rather than the official notice. Methods We collected French tweets posted between January 1, 2020, and March 31, 2020, containing anosmia- or ageusia-related keywords. Symptoms were detected using fuzzy matching. The analysis consisted of 3 parts. First, we compared the coverage of anosmia and ageusia symptoms in Twitter and in traditional media to determine if the association between COVID-19 and anosmia or ageusia could have been identified earlier through Twitter. Second, we conducted a manual analysis of anosmia- and ageusia-related tweets to obtain quantitative and qualitative insights regarding their nature and to assess when the first associations between COVID-19 and these symptoms were established. We randomly annotated tweets from 2 periods: the early stage and the rapid spread stage of the epidemic. For each tweet, each symptom was annotated regarding 3 modalities: symptom (yes or no), associated with COVID-19 (yes, no, or unknown), and whether it was experienced by someone (yes, no, or unknown). Third, to evaluate if there was a global increase of tweets mentioning anosmia or ageusia in early 2020, corresponding to the beginning of the COVID-19 epidemic, we compared the tweets reporting experienced anosmia or ageusia between the first periods of 2019 and 2020. Results In total, 832 (respectively 12,544) tweets containing anosmia (respectively ageusia) related keywords were extracted over the analysis period in 2020. The comparison to traditional media showed a strong correlation without any lag, which suggests an important reactivity of Twitter but no earlier detection on Twitter. The annotation of tweets from 2020 showed that tweets correlating anosmia or ageusia with COVID-19 could be found a few days before the official announcement. However, no association could be found during the first stage of the pandemic. Information about the temporality of symptoms and the psychological impact of these symptoms could be found in the tweets. The comparison between early 2020 and early 2019 showed no difference regarding the volumes of tweets. Conclusions Based on our analysis of French tweets, associations between COVID-19 and anosmia or ageusia by web users could have been found on Twitter just a few days before the official announcement but not during the early stage of the pandemic. Patients share qualitative information on Twitter regarding anosmia or ageusia symptoms that could be of interest for future analyses.