Alcohol-free wines are generally sweetened with around 40 g/L of added sugar to counterbalance sourness, which can be perceived as being excessive in such beverages. For young consumers who would consume alcohol-free products for health purposes, high levels of sugar could be an obstacle. The aim of this work was to investigate this target consumer’s appreciation of fully dealcoholised Chardonnay wines containing different levels of added sugar (0, 5, 10, 20 and 40 g/L). The results showed that liking significantly increased with sugar content, and that acceptability was only achieved in the sample containing 40 g/L of added sugar, with a liking score of between 5 and 6 on a 9-point scale. Liking scores were not affected by gender, information provided to panellists (specifically that they were evaluating alcohol-free wines), and level of wine knowledge. Those who gave the highest scores were occasional wine drinkers and daily soft drink consumers. Conversely, non-wine consumers and non-soft-drink drinkers gave lower liking scores. Though these insights need to be confirmed on more samples of fully dealcoholised wine, they can assist winemakers in developing alcohol-free products and in targeting the right young consumers.