The photo is about 1885 year.
Sitting in front, from left to right: Countess Isabelle of Paris (1848-1919) with youngest son Ferdinand (1884-1924), her mother Duchess Luisa Fernanda of Montpensier (1832-98) with Princess Louise (1882-1955), youngest daughter of Countess Isabelle.
Second row, from left to right: in profile at the very left Jean Duke de Guise (1874-1940) (3d son of Duke of Chartre), then Louis Philippe Count of Paris (1838-93), his brother Duke Robert of Chartre (1840-1910), Duke of Montpensier (1827-97), Princess Marguerite of Orleans (1869-1940) (2nd daughter of Duke of Chartre), her mother Duchess Francoise de Chartre (1844-1925), Princess Isabelle of Orleans (1878-1961) (3d daughter of Count of Paris), Princess Helene of Orleans (1871-1951) (2nd daughter of Count of Paris), Princess Marie of Orleans (1865-1909)(eldest daughter of Duke of Chartre), Princess Amelie of Orleans (1865-1951) (eldest daughter of Count of Paris), Infant Antonio of Orleans (1866-1930) (youngest son of Duke of Montpensier), Prince Louis Philippe of Orleans (1869-1926)( future Count of Paris),and with crossed arms Prince Henry of Orleans (1867-1901) (2nd son of Duke of Chartre
All things considered, I wonder wether the prince on the right beside Henri and Philippe is really Robert, son of Duke of Chartres? I don't think so anymore...
Why? Because this picture was taken at Eu Castle about 1885. Now Robert used to be in bad health. He never would go out of the château de Saint Firmin (his parents's estate near Chantilly), where he led a vegetative life under the care of Doctor Guéneau de Mussy, according Dominique Paoli ("Fortunes et infortunes des princes d'Orléans")
Born in Morgan House, near Richmond (G.B) on january 10th 1866, Robert d'Orléans died on may 30th 1885 to bronchopneumonia.
I think now the picture was taken after his death.
In such a case, this young man with a hat in his left hand before Amélie may be, as you thought, Antonio de Orleans y Borbon, infante of Spain, son of Duke of Montpensier. The two others
are well Henri (1867-1901) and Philippe d'Orléans (1869-1926)