The growing health problems of the world’s population related to inadequate nutrition have prompted many countries to take measures to develop healthy eating habits. One of the activities in the EU was the implementation of the School Fruit Scheme between 2009/10 and 2016/17, and School Fruit and Vegetables Scheme since 2017/18, in which fruit and vegetables have been one of the two components (the second component is milk and milk products). The aim of the article was to evaluate their effectiveness in terms of the consumption of fruit and vegetables in Polish families. The article was based on: EU legal acts, evaluations of the functioning and implementation of the schemes made by EU and Polish institutions, statistical data from Statistics Poland, and a review of the literature on the consumption of fruit and vegetables. It was found that despite the greater number of schools and children participating in the scheme and the growing expenses for its implementation, in most EU countries, including Poland, there is no increase in the consumption of horticultural products covered by the scheme (Pearson’s correlation coefficient between the number of children participating in the scheme and consumption in households between 2009/10 and 2020/21 amounted to −0.77). The reasons may be the weaknesses of the scheme (i.e., generally poor quality of products, too short duration of the scheme, and also insufficient involvement of parents in its implementation) on the one hand and the influence of other factors determining the consumption of fruit and vegetables under the scheme being difficult to statistically confirm (greater availability of other products, ineffective advertising) on the other.