FizzBuzz vs. FortRan
I find MODULO() to be jarring, when everything else is written in lowercase.  Be consistent.

To left-justify strings in the output, write it using a * format.  Since you want to write to standard output, you can simplify it by using print instead.

To left-justify numbers in the output, first convert it to a string, then strip leading spaces.

program fizzbuzz
implicit none
integer ::i
character(len=8) :: str

! Loop through integers 1 through 100
! Multiples of 3 print Fort
! Multiples of 5 print Ran
! Multiples of both print FortRan
! 15 is the lowest common multiple of 3, and 5
!    and thus is a shortcut to FortRan

do i=1,100
    if (modulo(i, 15) == 0) then
        print *, 'FortRan'
    else if (modulo(i, 3) == 0) then
        print *, 'Fort'
    else if (modulo(i, 5) == 0) then
        print *, 'Ran'
    else
        write (str, '(i8)') i
        str = adjustl(str)
        print *, str
    end if
end do

end program fizzbuzz