Here's an attempt; lowercase and uppercase Greek letters are upright, as uppercase Latin letters in math. Everywhere the Libertine font is used, which might give poor results in some cases, as its sidebearings are not really good for math.
\documentclass{article}
\usepackage[libertine]{newtxmath}
\usepackage{libertine}
\AtBeginDocument{\addfontfeatures{Ligatures=Historic}}
%%% Set up French style math
\makeatletter
\count@=`A
\advance\count@\m@ne
\loop\ifnum\count@<`Z
\advance\count@\@ne
\begingroup\lccode`x=\count@
\lowercase{\endgroup\DeclareMathSymbol{x}{\mathalpha}{operators}{`x}}
\repeat
% the next is for compatibility with LuaLaTeX
\providecommand{\Umathchardef}{\XeTeXmathchardef}
\AtBeginDocument{
\Umathchardef\Gamma = "7 "0 "0393
\Umathchardef\Delta = "7 "0 "0394
\Umathchardef\Theta = "7 "0 "0398
\Umathchardef\Lambda = "7 "0 "039B
\Umathchardef\Xi = "7 "0 "039E
\Umathchardef\Pi = "7 "0 "03A0
\Umathchardef\Sigma = "7 "0 "03A3
\Umathchardef\Upsilon = "7 "0 "03A5
\Umathchardef\Phi = "7 "0 "03A6
\Umathchardef\Psi = "7 "0 "03A8
\Umathchardef\Omega = "7 "0 "03A9
}
\@for\next:={alpha,beta,gamma,delta,epsilon,zeta,eta,theta,iota,kappa,lambda,
mu,nu,xi,pi,rho,sigma,tau,upsilon,phi,chi,psi,omega,varepsilon,
vartheta,varrho,varsigma,varphi}\do
{\expandafter\let\csname\next\expandafter\endcsname\csname\next up\endcsname}
\makeatother
\begin{document}
The story is about
$\alpha A \Gamma$ (αAΓ)
Math: $ABCDEFGHIJKLMNOPQRSTUVWXYZ$
Text: ABCDEFGHIJKLMNOPQRSTUVWXYZ
$\Gamma\Delta\Theta\Lambda\Xi\Pi\Sigma\Upsilon\Phi\Psi\Omega$
$I_{n}=J_{n}$
$\displaystyle\int_{\alpha}^{\beta}\Gamma(x)\,dx$
\end{document}
