When Spain took over Philippines, France had really other business on the continent and couldn't beat Spain to that (such as struggles with Habsburgs and Wars of Religion)
While it would be technically possible, afterwards, to have France ask for these, it would have make absolutly zero sense : it would have been far too isolated, compared to French navy priorities in Atlantics, to be sustainable at short term.
If you search of more French presence in the region, I'd suggest to take a look at Pescadores, which annexation or takeover was considered at the end of XIXth century, with the war with China especially.