I can't speak much to United States, but in Revolutionary France, the land-owning distinction reflects the kind of people who were chosen to the Estates General, and thus their values were reflected in the decisions of who was chosen to the later legislative bodies.

Start by looking at the Estates General and the kinds of people who would ultimately sit in it. The clergy was packed with nobility, the nobility had their own estate as well, and the Third Estate, that of the commoners, was filled not with poor rabble-rousers but by the kind of people who could campaign to be chosen, take time off work, and be expected to speak eloquently when called upon. So it's no surprise that the Third Estate is packed to the gills with lawyers, and to a lesser extent, other well-to-do new-money artisans, some of whom had been investing in titles and offices to cement their families' places in the economic pecking order.

So from the beginning, you have a body of people who have incentives to protect their station in life and aren't likely excited about handing government over to the whims of the mob. And among the political left (who will be in the driver’s seat for much of the years to come), you have people among whom Enlightenment thinking is fashionable. And big in these circles is 1) a belief in early forms of market economics and 2) a belief that property is sacrosanct.

This set of beliefs is going to be part of a cycle as the political class is focused on Enlightenment-inspired unwinding of old systems of despotism and naming and expanding civil rights, a current that will not concern the sans-culottes (the revolutionary poor) of Paris. The political class will expand political and civil freedoms, and the people of Paris will further radicalize

It's in these early days that the distinction between "Active" and "Passive" citizens arises. Active citizens are those who would pay three days' prevailing wages in taxes per year, and passive citizens were any citizens who paid less. And for the purposes of elections, these active citizens, (already the upper half of French men in terms of income) were merely the voters who picked electors to pick the people who would sit in the assembly, where property requirements were even higher.

The thinking in creating this distinction was that only those who had a suitable economic investment in the fate of the French nation could be trusted to be its dedicated stewards. So you'll see this distinction carry through to other aspects of life including, critically, membership in the French National Guard. Much like the legislative bodies that follow the Estates General, the National Guard is effectively composed of patriotic bourgeois citizens and similarly committed to these middle-class and new-money values.

But remember what I said about a cycle of increasing radicalization in Paris? That’s going to lead to universal manhood suffrage when Georges Danton leads an insurrectionary mob that takes over Paris, imprisons the royal family and sets up a standard by which the chief legislative body of France (which is going to change in the aftermath of this insurrection) is subject to the whims of the Parisian mobs. The following government will abolish the distinction between active and passive citizens and create a constitution the following year that would call for universal manhood suffrage. (It wouldn’t be implemented for reasons that are too complex to get into here but suffice it to say that all of France was effectively on fire.)

So the land-owning distinction for suffrage in France has its genesis in the propertarian liberals that would dominate the legislative bodies through the earliest phases of the revolution. Those distinctions would come to be abolished as the more radical Parisians take over the direction of the revolution. The current started turning further against propertarianism when you look at the Declaration of the Rights of Man of 1793 which still enshrined the right to property but with exceptions for “necessity,” which seem to correspond to later passages in the declaration that declare public relief to be “a sacred debt.” The Constitution of 1793 (to which this declaration was a preamble) would never be implemented but it indicated that France was going far enough left that it was moving beyond the “negative rights” sought by the original liberal members of the Estates General and National Assembly and were moving toward “positive rights” espoused by much of the modern-day left.

This only effectively answers the class distinction in voting rights and not the distinction of sex. And while there were early movements and changes in thought toward the liberation of women in the French Revolution, I’m unqualified to really go into why women’s liberation made the progress it did and stopped where it had. I hope this was helpful, though!