The Café Wars took place during the Algerian War, as a part of the internal fighting in France between two rival Algerian nationalist movements, the Mouvement National Algérien and the Front de Libération National (which later became the ruling political party in independent Algeria).
Since both organizations operated underground, and were wanted by the French government, the line between a military and a civilian target was hard to draw, and often wilfully disregarded by the combatants.
Groups from both the MNA and the FLN resorted to gangland-style killings, intimidation and the murder of civilians to pursue their political goals and secure finances and influence.
This led to the Café Wars being portrayed in France as acts of random terrorism, and conflated with attacks on French settlers in Algeria.
The FLN had by then routed the MNA's guerrilla units in Algeria, and for all practical purposes destroyed its organization in France.