No comments on this one yet, so I'll take a stab at it. The Franco-Prussian War impacted the Impressionists' work and the Impressionist artists individually in many ways, but one immediate effect was the death of Frederic Bazille (excuse the lack of accents). Bazille was drawn into the movement because of his friendship with Renoir, Monet, and Sisley, and soon began to paint his own original work. Aside from his quality as a painter, Bazille served as a patron and financial backer for the early Impressionists and provided a great deal of material support to get the movement off the ground.
In 1870, shortly after the outbreak of the Franco-Prussian War, Bazille enlisted in the French army and was killed in combat just a few months later. His death was a great tragedy for the early Impressionist painters, and he never got to see their first formal exhibition in 1874. Though his paintings are still widely known and appreciated, Bazille's short and unfulfilled career is one of the great what-ifs of art history. His early work showed tremendous vision and talent, but his work never had the opportunity to evolve like that of Monet, Manet, Degas, or the other impressionists.
From a financial stand-point, the Impressionists fell on hard times after Bazille's death, both because of the loss of their wealthy patron and due to general privation after the war. Ultimately Bazille's role as financial backer was assumed by Gustave Caillebotte, who also fought in the Franco-Prussian War. Caillebotte struck up a friendship with several of the Impressionist painters around the first impressionist exhibition in 1874 and actually began showing his own work in the second exhibition in 1876. Like Bazille, Cailebotte came from a wealthy family and had the means to support his struggling friends.
I realize that your question may be more about the war's impact on the Impressionists style or the themes of their work, which I don't have the qualifications to speak about, but I have always thought that Frederic Bazille's story was one of the great tragedies of art history, and it certainly impacted the lives of his impressionist friends.