A word for "false self confidence"

Suppose a motorbike driver jumped above 2 cars in a show, and a crowd of girls gave him an applause. He then tried jumping over 100 cars, and lost his life halfway by falling into the row of cars.

What do you say to this state of feeling, this false self confidence that he wasn't aware of its falsehood?

That sounds like the definition for the word hubris:

exaggerated pride or self-confidence

The whole situation—adulation and resulting recklessness—is probably most commonly summed up by "This went to his head." (Under what they label phrasal verbs, see "go to (one's) head," sense 2.)

I'm thinking he was "pumped" as in pumped up with confidence. Or he became reckless. His "ego was inflated by the adulation" - or was "egotistical." He became overconfident. Also, bold, or cocky, or cocksure would fit the situation.

I would probably describe such a person as foolhardy.

Cocky or cockiness both fit pretty well. Bravado is close, too. (The already mentioned hubris is perfect, but might seem too grand a concept in some contexts.)