I think we look back at the American and French Revolutions as primarily being about establishing democracy over monarchy. But when I look back at the reasons more in depth, they really seem to be more about taxation than anything else. Plus, the French Revolution in particular seems to have put in place some pretty anti-democratic institutions (Terror, Directory, and Napoleon). Even on the American side, Alexander Hamilton proposed making the US an elective monarchy.
Yet, I think it's difficult to doubt that desire for a democracy played some role. One of the key mottos of the American Revolution was "No taxation without representation", and that also influenced the French Revolution.
So how much did democracy influence these events?
You will find your answers in "Democracy In America" by Alexis De Tocqueville. But some form of Democracy was present in the American colonies even prior to the Revolution.
In America, Democracy (direct Democracy vs. Representative Democracy) has been an evolving thing since the days of the Continental Congress. Jefferson, Jackson, Lincoln and others right up to FDR and Lyndon Johnson have gradually increased the scope of direct Democracy (one person/one vote). However, America still has the Electoral College to select the President, and sometimes Representative Democracy still trumps direct Democracy (which is why G.W. Bush became President and not Al Gore). There are very interesting controversies going on right now as to how both the Democratic and Republican parties still use Representatives to select their Presidential nominees instead of using direct vote counts in the Primaries to determine the nominees.