What are the differences between French Symbolism poetry and Modernism?I have found a lot of similarities but I am running short on how to contrast...

That's tough because I would say that French Symbolism is
one branch of the much more broad category of Modernism.  Modernism covers not only a
historical period (roughly from early 19th century up until post WWII or the 1960s
depending on who you ask).  Modernism as a cultural and artistic movement, in my
opinion, includes many movements: Dada, Surrealism, Futurism, Fluxus, Happenings, Pop
art and Symbolism to name a few.  Modernism was all about the avant-garde, all about
rejecting tradition in favor of anything new.  Certainly revolutionary philosophies like
Marxism and Feminism were part of this grand scheme of rejecting tradition (and the
Enlightenment's claim of humanistic progress; we got the technological part down.)
Anything that pointed towards the future. Anything
progressive. 

Although Symbolism is a movement which
occurred during Modernism, you can still compare the two.  Symbolism, like Modernism,
was an attempt to get away from Realism and Naturalism in favor of a more abstract
artform. The Symbolists sought to use metaphoric language and images which symbolized
the essence of being. This essence was also beyond the scope of the senses, so the
senses themselves were mere symbolizers of being.  In general, Symbolism was more
abstract and imagistic than its antagonistic artforms: namely realism and
naturalism. 

Ok. One Big Difference: Modernism focused on
the alienation of the individual in the fast-paced technological world.  Some modernists
ignored technological advances in their work (except for Marinetti) as it was part of
the false Enlightenment project. So a lot of Modernist work was about the anonymity and
loneliness of the individual being pushed along passively, zombie-like as just a cog of
the masses in the machine of technological progress.  Symbolism focused on the
subjectivity of the individual and how to evoke abstract meaning by observing everyday
images and senses. Although different from Romanticism, Symbolism was similar in its
focus on the evocation of meaning through individual experience. So, it wasn't the
alienation of the individual or the individual's reaction to the external
world(Modernism); it was the subjective reaction, the internal, emotional
imagination(Symbolism).