If it's actually a 12v fridge (mostly made for marine installations), 400w solar should be able to handle it if you don't have other major draws. Boats generally don't have the option to use propane so they have put a lot of effort into getting these to run efficiently on 12v.
If you really meant 120v (household fridge), it's not so clear cut.
Either way, there should be a rated wattage draw while cooling and then you need to estimate the duty cycle. By multiplying out the wattage times the operating hours, you get an estimate of the watt-hrs used. Figure the 400w panels will put out about 1600 watt-hr per day but that presumes no shadows from trees or overcast. You can convert your battery bank to watt-hr by multiplying the amp-hr by 12v and assume 50% is usable without damaging the batteries.
If it's a household fridge, you can do the same but add another 10-20% because it needs to run thru an inverter to convert to 120v AC power. You could just buy a $20 killavolt meter which includes a kwh option. (It's good to have a voltage meter anyway so you can see at a glance if you have low voltage.