In my opinion, the French Revolution became so bloody because of the depth of the grievances that the revolutionaries felt and the level of stubbornness and rigidity that the people in power displayed. In other words, the revolutionaries were really angry and the people in power didn't want to give in to them in any way.
France had been ruled by one of the most absolute monarchies in Europe. This meant that the common people had been given little to no say in government. They had also been abused in various ways. Because of this, they felt strong grievances. Instead of trying to lessen that sense of grievance, the monarchy resisted the revolutionaries at every turn. This led the revolutionaries to feel even angrier.
So I pretty much blame the monarchy. They were too oppressive and too rigid. They did not give the revolutionaries anything and that made the revolutionaries violently angry and let the radicals come to power.