For example the parties: LR PS FN
And is it the same gender for all parties? What about "UDI" can you use l'UDI ?
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The gender of the underlying words is kept, i.e. Le PS (Le parti socialiste), Le FN (le front national). Most are masculine, an exception is LS (La ligue du sud).
Note that no article is prepended when one is already present like LR (Les républicains), or in some other cases like EELV (Europe Écologie Les Verts), DLF (Debout la France) or LO (Lutte ouvrière).