Aller (to go) and faire (to do/make) are both highly irregular but essential, since aller builds the near future and faire appears in dozens of everyday expressions. Aller: je vais, tu vas, il/elle va, nous allons, vous allez, ils/elles vont. Faire: je fais, tu fais, il/elle fait, nous faisons, vous faites, ils/elles font.
Faire shows up in weather (il fait beau, the weather is nice), sports and activities (faire du sport, faire les courses), and causative constructions (faire + infinitive, to have something done). Nous faisons is also a rare spelling case — the ai is pronounced like an "e" sound, unlike anywhere else in the conjugation.