Summary: I can find information about the total number of fatalities, but I don't find anything on the number of paramotoring trips taken. Without that, I cannot make any fair comparison to any other form of personal aviation.
The US Powered Paragliding Association has publicly available records listing 27 fatal paramotoring incidents going back 20 years or so. Looking around their website did not give me the impression that this was rigorous or high-quality data. Although they have an accident investigation team, it seems woefully underfunded. I am willing to believe that they have missed some number of fatal incidents.
A 2015 fatality report lists 10 paragliding fatalities. This was put out by the US Hang Gliding and Paragliding Association. Although it isn't about paramotoring, I think their numbers are more reliable.
There should be some similarities between accident rates. This study looked at the first data set I linked and found that the engine caused 11% of all incidents. I assume that a large fraction of the other 89% could happen on an unpowered paraglider. I can also assume that having an engine can save you from certain types of accidents.
You asked about the rate of fatalities, not just the number. I cannot find any estimates of the number of trips taken each year, or even any information on the number of members the USPPA has.
If you can find some information on the number of trips taken every year, you can compare those numbers to the rate for personal planes, which cause fatalities at a rate of 2 deaths per 100,000 pilot hours (Page 41).