Two French Revolution questions in one day? But it's not even my birthday!
First and foremost: Working-class and petty-bourgeois women were heavily involved in all of the major protests and uprisings over the course of the Revolution. This was not new to the Revolution. In fact, prior to the Revolution, popular protest was a female-dominated activity. This is because most uprisings were subsistence riots, and provisioning (that is, going to shops and markets to acquire food for a household) was a female activity. For more on this see *The Flour War* by Cynthia Boutton; it's an account of the grain riots of May 1775, which are considered to be the last major uprising in France before the Revolution.
One of the things that differentiated the Revolution from these past movements was, in fact, the large number of men involved. Where during the Flour War women were known to push men out of the action, telling them that this was "women's business" and none of their concern (I don't have a page reference for this, sorry - I'm at work and my books are at home), men were actively involved in the popular side of the Revolution, sometimes even more so than women. The major exception to this is the October Days, when the women of Paris marched to Versailles to bring the king and his family back to the capital. As this began in the markets - a largely female sphere - most of those involved were women. Commentators in Britain had such a hard time accepting women's involvement that the myth quickly arose that these were mostly men in drag!
We don't know the names of the women who participated in these events (nor, indeed, most of the men). We do know of a few women - largely members of the elite - who were involved with the Revolution, mostly in its early stages. Olympe de Gouges, Théroigne de Méricourt, Germaine de Staël (daughter of Jacques Necker), and Madame Roland (wife of Jean-Marie Roland) are the best-known. All of them published writings in support of the Revolution, some of them specifically advocating for women's increased political participation in the new government. Out of all of them de Gouges is probably the most significant: her Déclaration des Droits de la Femme et de la Citoyenne (Declaration of the Rights of Women and the Female Citizen) is an important proto-feminist text. It was written in response to the Declaration of the Rights of Man and the Citizen, with the goal of extending those rights to women. De Gouges also had some radical ideas about marriage and the rights of illegitimate children.
Early on, she and her compatriots had reason to be optimistic that their goals would be realized, but that optimism didn't last. All of these women fell out of favour as the Revolution moved into its more radical stages. De Gouges and Roland (both Rolands, in fact) were executed in 1793. Madame de Staël lived out the majority of the Revolutionary decade in exile, and Théroigne - the most radical of the four - was subjected to repeated attacks from both sides of the political spectrum, suffered a mental breakdown and spent the later years of the Revolution in an asylum.
In the end, women did not make significant gains during the Revolution. While the Ancien Régime had disenfranchised the majority of its population, the importance of kinship ties (and therefore reproduction / sexuality / childbirth) in monarchy and aristocracy meant that women had a clear and important political role. The creation of citizenship as the prerequisite for political participation removed that, as citizenship was defined as exclusively masculine. Additionally, many aristocratic women exercised significant power "behind the scenes" as the wives, mothers or mistresses of prominent men. This role was specifically and deliberately demonized during the Revolution, and female political participation portrayed as a symptom of a corrupt government. Women's participation in the public sphere - even through popular protest - lost the legitimacy it had once had. While universal male suffrage was first granted in 1792 (and repealed a few years later, and re-instituted a few decades after that, etc. etc.), women did not get the right to vote in France until 1945.
EDIT: If anyone wants sources let me know; I can add citations when I get home.