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Perhaps it would be a good idea to get away from looking for a noun/adjective equivalent, and use something like "by taking an individual approach to the management of..."
Clearly, the idea is that the spaces should be as natural as possible, so ecological, sustainable, thoughtful, reasoned... I suppose you can't really have "natural management", can you?
Your suggestion of adding a word such as ''sensitive'' or ''thoughtful'' fits with the definition of ''gestion différenciée'' given on Wikipedia:
La gestion différenciée (parfois qualifiée de « gestion harmonique », « gestion RAISONNÉe durable», « gestion évolutive durable », « gestion RAISONNABLE » selon les villes, et même de gestion raisonnable 1en Isère) est une façon de gérer les espaces verts en milieu urbain qui consiste à ne pas appliquer à tous les espaces la même intensité ni la même nature de soins.
one word may not be enough. Clearly the approach is "ecological" and probably sustainable (though sustainable doesn't necessararily exclude "traitements phytosanitaires"). I suggest adding the word "sensitive" to sustainable/ecological, etc. This implies that the planners have at least given it some thought. Or "thoughtful", even.
vu dans la déf. de clain. On veut faire évoluer le modèle standard vers un modèle qui s'adapte à un environnement précis et aux diverses circonstances qui l'accompagnent (usage, personnel ...)
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6 mins confidence: peer agreement (net): +2
differentiated management
Explanation: The above is widely used, or perhaps you could try using "by adopting a different management approach" in plainer English.
The translation workplace 
peer agreement (net): +2