The only maximal affine Hadamard family stemming from the Fourier matrix $F_8$ is the $5$-parameter self-cognate orbit $$F_8^{(5)}(a,b,c,d,e)=F_8\circ{\rm EXP}\left(i R_{F_8^{(5)}}(a,b,c,d,e)\right),$$ where $$F_8=\left[\begin{array}{llllllll} 1& 1& 1& 1& 1& 1& 1& 1\\ 1& w&w^2&w^3&w^4&w^5&w^6&w^7\\ 1&w^2&w^4&w^6& 1&w^2&w^4&w^6\\ 1&w^3&w^6& w&w^4&w^7&w^2&w^5\\ 1&w^4& 1&w^4& 1&w^4& 1&w^4\\ 1&w^5&w^2&w^7&w^4& w&w^6&w^3\\ 1&w^6&w^4&w^2& 1&w^6&w^4&w^2\\ 1&w^7&w^6&w^5&w^4&w^3&w^2& w\end{array}\right]:\quad w=\exp\frac{2i\pi}{8}$$ and $$R_{F_8^{(5)}}(a,b,c,d,e)=\left[\begin{array}{llllllll} \bullet&\bullet&\bullet& \bullet&\bullet&\bullet&\bullet& \bullet\\ \bullet& a& b& c&\bullet& a& b& c\\ \bullet& d&\bullet& d&\bullet& d&\bullet& d\\ \bullet& e& b& c - a + e &\bullet& e& b& c - a + e \\ \bullet&\bullet&\bullet& \bullet&\bullet&\bullet&\bullet& \bullet\\ \bullet& a& b& c&\bullet& a& b& c\\ \bullet& d&\bullet& d&\bullet& d&\bullet& d\\ \bullet& e& b& c - a + e &\bullet& e& b& c - a + e \end{array}\right].$$