1st arrondissement supermache and packed lunches

Staying literally across from Louvre and Palais Royal, really looking forward to walking and enjoying the area!

which supermache would you recommend for a few things in our apartment, as well as where can i get a picnic style lunch prepared for a few days of touring we are doing (gold cart booked for 3 hours at Versaille so lunch in a garden would be lovely (taking my 82 yr old mum on a nice lunch mid day) and another day of parks to slow down and enjoy the paris offerings.

which park would you recommend that is not at the Eiffel Tower, but further away with a great view of the tower?