Groguhé was born on November 9, 1962 in Istres, France. The daughter of Algerian immigrants, Groguhé was one of twelve children. She has a Master's degree, practiced as a psychologist, and did community work. In France, she worked in the area of social and occupational integration for youth and adults in distress. Trained in transactional analysis as a therapeutic tool, she held sessions as a trainer. Groguhé was chair of the Istres equality association. She ran as an independent candidate in 1994’s cantonal election. Noticed by Jacques Siffre, Istres’ socialist mayor, she ran municipally in 1995. Groguhé was elected and was a municipal councillor from 1995 to 2000. She was responsible for integration, and left her position after the birth of her children. Groguhé and her husband, who is originally from the Ivory Coast, decided to leave France so their children would not be discriminated against because of their background. They submitted their visa requests in 2003 and immigrated to Canada in 2005.
Federal politics
Naturalized in 2010, Groguhé joined the New Democratic Party. She was a candidate for the party in the 2011 federal election in the Montreal riding of Saint-Lambert and defeated the incumbent Bloc MP, Josée Beaudin, by receiving 42.65% of the vote. After her election, Groguhé was appointed the NDP’s assistant critic for immigration, citizenship, and multiculturalism. Following Jack Layton's death, she supported Thomas Mulcair in the 2012 NDP leadership race. From April 19, 2012 to August 12, 2013, Groguhé was the Deputy House Leader of the NDP and the Official Opposition. She then became the NDP's Deputy Whip, which meant she was also the Official Opposition Deputy Whip, and gave up the assistant critic portfolios she had held since 2011. In June 2014, the Board of Internal Economy found that a group of NDP MPs, including Groguhé, had improperly used Parliamentary resources for partisan activities by sending out nearly two million mass mailings, costing 1.17 million dollars to different ridings, including some that were holding by-elections at the time. Groguhé kept the deputy whip position until she lost her bid for re-election in the new riding of Longueuil—Saint-Hubert in the 2015 federal election.