For a very laid-back picnic spot I recommend Canal Saint-Martin. Starting at metro République level and moving northwards, you will cross many cafés and take-away lunch spots, at least one person playing acoustic guitar and Jardin Villemin (for those who prefer a grassy enclosed area that is safer for kids). Further along, the Canal turns into Bassin de la Villette. This is where everyone plays “pétanque” in the evening and where I gather with friends for picnics before heading to one of the bars or nightclubs nearby.