/ə/ is the pronunciation given by TLFi, so in theory it should be used. However, in practice, this may change to /ø/ or /œ/ depending on the speaker and the context in which the schwa appears. This is discussed in detail on English Wikipedia. In particular:

Fagyal, Kibbee & Jenkins (2006) state, more specifically, that it merges with /ø/ before high vowels and glides […] in phrase-final stressed position […] and that it merges with /œ/ elsewhere.

[…] Pronouncing [ə] as [œ] is a way to emphasise the syllable.

The exact pronunciation of the schwa is addressed in a number of academic papers, including in "On the phonetic identity of French schwa compared to /ø/ and /œ/" by Fougeron, Gendrot, and Bürki.

This variability in the phonetic identity of schwa has in fact been reported in many descriptions in the literature. Its pronunciation has been said to vary between [œ] and [ø] depending on speakers, varieties of French, and segmental contexts (Delattre 47, 64; Tranel 87, Valdman 70).