Excel formula to search if all cells in a range read "True", if not, then show "False"

You can just AND the results together if they are stored as TRUE / FALSE values:

=AND(A1:D2)

Or if stored as text, use an array formula - enter the below and press Ctrl+Shift+Enter instead of Enter.

=AND(EXACT(A1:D2,"TRUE"))

As it appears you have the values as text, and not the numeric True/False, then you can use either COUNTIF or SUMPRODUCT

=IF(SUMPRODUCT(--(A2:D2="False")),"False","True")
=IF(COUNTIF(A3:D3,"False*"),"False","True")

=IF(COUNTIF(A1:D1,FALSE)>0,FALSE,TRUE)

(or you can specify any other range to look in)