Is it marked on the label? Yes, it is mandatory as soon as a product contains more than 0.9% GMOs. In general, the mentions are embedded in the list of ingredients (ex:from genetically modified soy). apart from soybean oils, supermarket products do not directly contain GMOs. But about 80% of farm animals are partly fed with GMOs, and this is not reported on the products from these animals (meat, eggs, etc.). And when a label bears the words "GMO-free", it means that the GMO threshold does not exceed 0.1% (controlled by the DGCCRF).
If it's organic, is it safer? Yes, it is even the best guarantee to avoid GMOs (in ingredients and in feed for farmed animals). A damper ? As soon as GMOs are grown, neighboring crops can be contaminated (there may be residual traces, but nothing to freak out about).
And for the vegetables? There, a priori, we are quiet. No transgenic fruit or vegetable is currently authorized for sale in the European Union.
Beware:products imported from the USA, Canada, Argentina or Brazil and containing soy, corn or rapeseed, which are the plants most often genetically modified.
Thanks to Rachel Dujardin, GMO Campaigner, Greenpeace.