First one was a revolutionnary state. Depending of the faction in power, it changed things a lot.
With Montagnards, it was an anti-elitist, regime of war (more because being attacked than actual warmongering). Mix of urban popular and little bourgeoisie interests.
With Thermidoriens, more upper bourgeois and big land-owners.
With Bonaparte, more importance given to rural landowners and military, as well little bourgeoise (with recuperation of former Montagnards.
It's not really ONE regim, more some following each other.
The Second Republic was something like that as well.
First, an uneasy alliance between little bourgeoisie and workers, then rural land-owners (led by big ones) and industrial bourgeoisie that culminated into the II Empire.
The third Republic was at first concieved as a transitional regime to reinstaure the monarchy in France. So it gave little power to executive, the monarchist hoping to stay majoritary in the chambers (thanks to war and fraud, they managed to be majoritary in 1870).
It was institutionally a conservative regim, not allowing big institutional reforms and the turnover of radical ideologies (radicals, left radicals, socialist) is partially explained by that.
Basically a constant struggle between progressists and conservatives with the first being supported by upper workers, little land owners and little bourgeoisie, the other by big landowners, industrial and financial bourgeoisie, army and clergy.
It was uneasy to remove something applied by a majority, whatever which one, so the result was more a patchowrk than a planned feature.