Food labeling can influence, sometimes facilitate, changes in consumer diets to support environmental sustainability and in response to climate change. However, a significant impediment to this dietary shift may arise from the consumers’ tendency to underestimate the environmental impact of their food choices and from their limited knowledge about sustainable certifications. These aspects are influenced by the characteristics and geographical affiliations of individuals. In such a context, the aim of this research has been to identify the main factors that drive the food purchasing frequency and the changes in food consumption associated with consumers’ concerns about climate change and interest in sustainable food certifications by comparing different food products and countries (Italy, France, Germany, Denmark, the USA, and China). A cross-country survey was conducted on 6500 consumers of various food products. The obtained mean scores were then compared, using generalized linear mixed-effect models, to evaluate the associations between the consumers’ food purchasing frequency, the importance of sustainable certifications, and changes in food consumption due to climate change concerns. Much of the variation in food consumption, purchasing behaviors, and interest in sustainable certifications was found to depend on such factors as age, gender, and country of origin. Indeed, Chinese consumers exhibited a heightened interest in sustainable food certifications, yet their consumption scores for all food products overall were higher. Conversely, adult and elderly Danish consumers demonstrated a decrease in the consumption of cheeses, meat, fruits, and vegetables, and their interest scores in all sustainable food certifications were lower. Despite the challenges posed by various consumers’ interests and minimal changes in food consumption patterns, our findings suggest that sustainable certifications present a promising avenue for straightforward interventions to promote the adoption of sustainable diets and to address climate change.