Here is how Wiktionary defines オブジェ in the context of art:
表現の対象となるもの、前衛美術では，幻想的効果のために取り入れられる物体。
My very hesitant attempt at a translation:
It depends on the represented target, but in avant-garde art it is an object that has been transformed in order to produce an illusionary effect.
Here is another, (but similar,) approach... but combining both possible definitions of "objet" in the original context:
表現の対象となるもの、前衛美術では，幻想的効果のために取り入れられる物体。
An expression transformed into an object (used to surreal effect, in avant-garde art.)
Note: "surreal" is used here to demonstrate a different approach for that part of the translation, though, something having to do more with the word "illusion" would probably be more accurate.
Also, (and as already noted in the comments on the question,) this part: It depends on the represented target, doesn't seem to be in the original writing.
As long as the definition fits with the definition of "objet" in French, the translation into English should be fine.
A target of depiction. In avant-garde art, an object introduced to create an illusory effect.
This might not be the best translation, but it avoids the pitfalls that others seem to have fallen into.
The first comma is a listing comma separating two definitions of the word.
となるもの doesn't have much meaning, except for maybe taking an fairly abstract word (対象) and explicitly creating an instance of it.
幻想的 I find hard to translate, since I feel it's somewhere between "dreamy" and "illusory", both of which have slightly different connotations in English.
