In 2005 she graduated from the School of Visual Arts, where she majored in Film and Video.
Robespierre began her career working as a production assistant on big budget features like American Gangster. She also worked for the Directors Guild of America until 2014. In 2009 Robespierre co-wrote (with Anna Bean and Karen Maine) and directed the short film Obvious Child, about a young woman who is impregnated after a one-night stand and decides to have an abortion.
Robespierre approached Jenny Slate to star in the lead role after seeing her perform at a comedy club
Robespierre later expanded the short into her 2014 feature film debut Obvious Child with Slate once again playing the lead role. The film premiered at the 2014 Sundance Film Festival where it was acquired by A24 Films.
In early 2015 Robespierre announced she was developing a comedy pilot for Fx with Elisabeth Holm, who co-wrote Obvious Child, starring Jenny Slate and Ari Graynor.