He saw a parking space . . . . . . . . two cars and drove . . . . . . . . it.

The most common use of 'between' is when something is in the middle of two things or two groups of things. It is sometimes used in the phrase in between. First blank will take 'between'.
When someone or something comes from outside to the inside, we use the word 'into'. Here the car comes from outside to inside of the parking area. Second blank will take 'into'.