What is an English word which means 'bêtement'?

Bêtement is a French word whose literal meaning is 'in the manner of an animal'. It is often used metaphorically, to describe an action carried out in a robotic fashion – without thinking. How would you translate this sense into English? Perhaps robotically is the answer, but can anyone think of anything better?

Bêtement has other meanings than the one you are referring to, but in this case, when you do something without thinking, you do it mindlessly.

"She mindlessly passed me on the street without even giving a hint of recognition."

"I have been mindlessly driving to work everyday, and never noticed that our beloved oak tree was gone."

mindlessly: Giving or showing little attention or care; heedless.

You might consider the French phrase Que je suis bête ! to mean "I am stupid!" (Am I stupid!), but a more subtle meaning might be "What was I thinking!" which is a short distance from "I wasn't thinking". In other words, "I was acting mindlessly" ( Je me comportais bêtement ) .

"Bêtement" is by no means associated with ideas of insanity, and even less of bestiality.

It is a very mild word to say "foolishly".

"Zut, j'ai bêtement oublié mes clefs !" = "Oops, I have foolishly forgotten my keys !"

and "tout bêtement" means "quite simply"

"Alors, je suis rentré tout bêtement par la fenêtre". = "Then, I quite simply went in through the window".

and "une bêtise" = a not really important blunder.

A Franco-British

The most common animal metaphor relevant here is that of cattle - so you can say in a bovine manner thus denoting their dull and stolid mechanical nature.

Bovine is apt in this figurative sense. Continuing the animal metaphors you may prefer mutton-headed, which basically carries the same meaning of being dull and slow-witted.

A good non-animal robotic metaphor is automaton-like.