Initially, the robot will not go on the streets on its own, but will be followed by an operator because Franprix does not have permission for the machine to travel solo yet.
For that, legislation needs to be changed, Mochet said, adding he hoped that would happen soon.
In future, Franprix and TwinswHeel hope customers will be able to order goods online or in store, and the droid will take them to shoppers' homes and announce its arrival by text.
The message will include a code so customers can unlock the robot's suitcase and unpack the goods.
Larger robots could also be used by store staff to re-stock shelves.
Franprix, which made 1.6 billion euros ($1.8 billion) of sales last year from its network of 900 stores, is not alone with its experiment.
Last year, U.S. grocery giant Kroger launched an automated delivery trial in partnership with driverless delivery firm Nuro. Having completed the first phase in Scottsdale, Arizona, it recently announced plans to transfer the programme to Houston, Texas.
In Britain, Tesco and Co-op are testing a six-wheeled delivery robot in Milton Keynes with Starship Technologies.
($1 = 0.8850 euros)