On closer inspection, the lines appear fraught with ambiguity. In the French newspaper Libération (20.03.2008), Bashung said
[Bleu pétrole] est peut-être un album humblement politique (...)
I.e. possibly a humbly political album. So, naturally, people looked for a political interpretation of the song "Résidents de la république".
For example, pink ("rose" in French) is the colour of the Parti socialiste / Socialist Party.
But what does the colour blue stand for? Some have suggested the UMP, whose colours are blue, white and red, i.e. not only blue.
Another possibility (not found among the comments and interpretations I read) is that the line alludes to the right-wing MR / the Radical Movement, whose colour, mauve, looks like pink with a shade of blue. In fact, Wikipedia notes that
Many pale wildflowers called "blue" are actually mauve.
The political significance of "le rose a des reflets bleus" might then that the MR's extreme position rub off on even the French Socialist Party, but I can't find any concrete evidence to support this.
Note that on maps representing presidential election results, pink is used to represent departments where the socialists won, blue for UMP and a darker shade of blue for MR.
See, for example, the 2002 presidential elections and the 2007 presidential elections. So blue is ambiguous from this point of view.
On Yahoo Questions/Réponses, someone suggested that "résident" might refer to carte de résident, a type of resident card that foreigners can apply for if they want to stay in France for ten years or longer. The implications of this are not explained.
Someone even suggested (in a YouTube comment) that pink stands for the monarchy and blue for the republic.
However, if either of these colours can be associated with the French monarchy, it would be blue rather than pink, since blue was the background colour of the Kingdom of France's flag.
(Heraldry used a limited set of colours or tinctures and pink is not one of the traditional tinctures.)
In addition, the accusation that Emmanuel Macron, elected President of France in 2017, seems to think of himself as the new Napoleon, is much more recent than Bashung's song and therefore irrelevant at the time when it was written.
Catherine Armand, who runs a website about French chanson, suggested in her article Résidents de la République – Alain Bashung (22.08.2014) that the song can be seen as political or as a sort of testament.
According to the political interpretation, citizens have been degraded to residents, who have become powerless pawns. The Socialist Party then represents "la gauche caviar" ("the caviar[-eating] left") who has betrayed the people (with blue representing the UMP).
However, when reading "Résidents de la république" as a personal song ("chanson testament", since Bashung already knew he had cancer and would die one year later), she does not provide an explanation for the colours.