Europe committed to reduce greenhouse gas emissions (GHG) by 40 % by 2030 from 1990 levels. Food emits about 30% of all GHG, the major toll arising from animal products (half of food GHG). This urges the necessity of public actions to encourage sustainable diets. Food policy is now at the double stake of preserving environment and improving health. To implement a public policy combining environmental and nutritional issues in a socially- conscious framework, a food demand study and the potential substitutions between foods is necessary. This article aims at offering a solid base for such policy decisions. Which are the food groups more suitable for a price change? Where are the more disparities in price responsiveness among income classes? Are own-price effects the only relevant? Do cross-price effects matter? To study food demand, we estimate an EASI demand system. It is based on a pseudo panel of 8112 observations constructed from Kantar panel data (1998-2010). It registers French households purchases for food-at-home. We add the nutritional content and Greenhouse gas emission related to foods through Life Cycle Analysis. For 21 food groups, built according to their environmental and nutritional characteristics, we run expenditure and price elasticities. Based on these results, two taxation scenarios are implemented. For each we increase by 20% the prices of food categories with most adverse effects on (1) environment only (ENV) and (2) both environment and health (ENV-NUT). The ENV scenario induces more reductions in environment impact than the ENV-NUT scenario, in particular for SO2 emissions. A greatest impact is observed for lower-average income households and with a household head less than 30 years old. However, undesirable nutritional effects lead to consider the necessity of a trade-off between environment and nutrition. Our conclusions find that this trade-off is not so costly (-18% in terms of CO2). Moreover, our results give new insights for targeting public policies toward the youngest households which we find more sensitive to prices and which are at the beginning of the consumption life-cycle.