IMO, A is correct.
A)The footwear and apparel brand founded in 1914, Brooks Sports
has for most of its history
made shoes for a variety of sports, but in 2000 it narrowed its focus considerably to concentrate on running shoes.
Correct. Present perfect: has made shoes... is correct.
B)Brooks Sports, the footwear and apparel brand founded in 1914,
has for most of its history
been making shoes for a variety of sports, but in 2000 it considerably narrowed its focus to concentrate on running shoes.
Wrong. Present perfect continuous is not necessary
C)The footwear and apparel brand founded in 1914, Brooks Sports, has for most of their history made shoes for a variety of sports, but in 2000
they narrowed its focus considerably to concentrate on running shoes.
Wrong. S-V problem.
D)The footwear and apparel brand founded in 1914, Brooks Sports, has for most of their history made shoes for a variety of sports, but in 2000
they considerably narrowed down its focus to concentrate on running shoes.
Wrong. S-V problem.
E)Brooks Sports, the footwear and apparel brand founded in 1914,
had for most of its history
made shoes for a variety of sports, but in 2000 it narrowed its focus considerably to concentrate on running shoes.
Wrong. Past perfect is not necessary