Home PC power problem caused by fridge
Depending on where you live;  the answer to this question will vary. 

If you live in a country that actually has 230V 30A plugs (which I'd class as unusual!)  you have a total power budget of 6900W to work with.  

Plugging in two 1200W UPS batteries is well under this budget;  but keep in mind that you need to avoid going over (typically 70%) of the "peak" load that this breaker will supply;  or around 4900W. 

1200W * 2 = 2400W.  (Obviously;  keep in mind that these devices are rated to 1200W Max;  so they will generally only consume anywhere near that when the power has actually gone out and the batteries are discharged.)

TLDR: 
If what you have now works;  adding a UPS or two is unlikely to add significant load to the system;  except immediately after power outages. once your power comes back on;  you may trip the breaker if you have a lot of other power-hungry devices also plugged in and left on. 

I'd recommend you contact an electrician rather than ask this online;  they will know your local code much better then we will and will be able to answer questions like this. 



For the record: a 32A breaker is very unusual where I live and work; (which is much of North America and significant parts of Europe!)  Given that the breaker you listed is rated at the specific ampacity at such a low operating temperature (30 degrees C) I imagine your local electrical code has derated that value to a more practical temperature rise.  Without knowing the local code;  I cannot confidently say what power that breaker is rated for. 

You mentioned "fuse" which is the wrong term for the circuit breaker you linked to;  a "fuse" is permanently destroyed when an over current condition occurs;  where as a breaker mechanically (typically) disconnects the circuit in response to an overcurrent situation.     A breaker can generally be "reset"  while a fuse must be "replaced".