A refrigerator compressor can consume 30W, or it can consume 300W. If there is a defroster, that can be as much as 800W.
Defroster would run 30 minutes or less per day. Compressor runs as little as a few hours per day to continuous.
You have to determine how much power consumed to size the system.
Start with the label, which lists watts and amps.
Look up a consumer energy label that estimates power consumed per year, e.g. 630 kWh/year. Divide by 365 to get daily consumption, e.g. 1.726 kWh or 1726 kW.
You could size battery to power that load for one 12 hour night, or for 60 hours without sun to cover two cloudy days.
Find an "insolation" calculator on-line that says how much sunshine your location gets, and what angle tilt of panels is optimal (or use the tilt of your roof, if to be mounted there.)
Summer gives more effective hours, winter fewer, like 7 vs. 2 hours for some locations. That lets you calculate how much PV panel needed.
There are some efficiency losses, so maybe 40% more needed.
Actual power consumption will vary with temperature and run-time of refrigerator.
You can get away with really small batteries if you run generator for those days not enough sun. And turning off inverter at night; frozen foods should stay cool until morning.
Automotive batteries usually aren't good for deep cycling. These claim surprisingly good cycle life, like 800 cycles to 80% DoD, so might last 2 years draining 80% each night.
2x 100Ah x 12V = 2400 Wh. Could configure as either 12V or 24V system without needing more batteries.
2400Wh x 80% = 1920Wh usable. 1920Wh/12 hours = 160W average load (compare to your calculation of consumption from energy label for two refrigerators.)
If you turned off inverters each night, then the batteries could last a decade.
If you turn off a power strip (or electronic timer) at night and leave inverter running for other loads, "no-load" power draw of inverter presents a drain on batteries. Might be 20W, might be 150W; this parameter matters for small systems. It is also a drain during the day, affects needed PV array size.