If it's launching mid-month then it won't be the ps+ game, and if it isn't the PS+ game immediately it will most likely be a long wait until it is, if at all.

PS+ games for PS4 so far have all been released alongside the games initial release (nothing has been on the store, then been free on plus a week after). Probably because Sony don't want to anger consumers who buy the game, and then make it free one week later.

You can usually spot ps+ games if they detail their release date as being over the start of a month. (As was the case with Deadnation, Outlast, Resogun and Contrast).