Yes. The 1km radius limit only applies when you are outside to get some exercise (such as going for a jog, walk, or walking the dog).
You will need an attestation exemption form, which is available to print and download here (in French). There is an English version available and also an easy-read version with pictograms. There is also a digital version available via the TousAntiCovid smartphone app.
You will need to tick the second box down on the attestation form, which says “des achats de première nécessité” (necessary purchases). or food and basic necessities, or the box that says "pour faire mes courses". This permits you to be away from home for more than an hour and travel beyond the 1km limit.
Most of the major supermarkets and many other stores have put in place click-and-collect options, allowing you to order groceries online and arrange to pick them up at a certain time to limit contact and reduce the spread of Covid-19.
Non-essential items will not be available at the supermarket, as announced by Prime Minister Jean Castex today with more details set to be announced tomorrow.