Rwanda was already in the midst of a civil war prior to the beginning of the Genocide.
Paul Kagame's RPF had invaded from Uganda in 1990, the RPF was largely composed of Tutsi Diaspora who had fled to Uganda following anti-Tutsi pogroms in the late 1950's. The diaspora had close ties to Ugandan leader Yoweri Museveni and had formed a significant part of the forces that won him control of Uganda (Ugandan Bush War).
There was basically an entire (Diaspora anglophone) Tutsi brigade in the Ugandan army which deserted en-masse to invade Rwanda in 1990. The fighting was inconclusive, there were a series of truces from 1992 on while peace negotiations took place, punctuated by RPF offensives and. On the eve of the genocide the RPF controlled a small area of territory in Northern Rwanda.
Following the assassination of Habyarimana and the beginning of the genocide the RPF renewed their offensive, FAR (Rwandan army) resistance was ineffective, and the gradually took over the country, despite a French military intervention on the side of the FAR.
The Interahamwe and FAR fled because the RPF gained effective military control over the entirety of Rwanda.
The extent of the genocide and the scale of the counter-genocide killings by the victorious RPF are hotly contested, as is the role of the French intervention and the question of whether it prevented or abetted further genocide in the area under French control.