As well as being partial to a Chinese, I do love my Mexican food (mole is simply to die for!). Are there any authentic ones within 45 minutes of Beauvais?
Le ToucoNot sure how authentic it is for your tastes, but you've got Le Touco, 7 rue de Buzanval, 60000 Beauvais. Tel: 03 44 15 01 41. So should be on your doorstep. We've eaten there once and enjoyed it. Check the various reviews from Google and see what you think. It's in the town centre, is spacious, and has a bar at the front with the restaurant area behind. Spacious and well lit. Reasonable atmosphere, and I think they get involved with the various music festivals that Beauvais holds and may even hold concerts there.
I was surprised to find that there's no Mexican restaurants in Picardy at all listed on Trip Advisor. These guys are potentially missing a trick.