Here is the first similarity: massive loss of life, especially in the ruling class. King Louis XVI and his wife Marie Antoinette both were beheaded and Czar Nicholas II and his family were shot to death. Many lesser nobles and pro-government generals were killed in purges during the French Revolution and Russian Revolution.
The second similarity is that both revolutions led briefly to a period of the nations trying to form republics. The initial leadership of Russia sought to strengthen the Duma (Parliament) and give the people more of a voice. However, the pressure to stay in WWI by the Allies brought down this government and opened the door to civil war where the Bolsheviks took over the government and Lenin passed draconian laws. France also formed a republic but it was soon toppled and after the Reign of Terror, Napoleon set himself up as supreme leader.
Lastly, both were caused by governmental inefficiencies. France had an unbalanced taxation system that put more pressure on those who could barely pay, and the economy was poor due to a long series of wars with Britain, most recently the American Revolution. In Russia, infrastructure such as rails were the worst in Europe and were hampering the movement of men and material for the WWI effort. People were starving, both civilians and soldiers. Both governments were seen as the root of the people's problems, and Louis XVI and Nicholas II were not forceful personalities who could put down resistance with progressive reforms or force.