So based on what I’ve seen on the forums I’ve come up with a few nicknames/call out names you can call the new character when you see him in a game.
-Baps
-Daddy
-Fortnite
-Not a black woman
-Demoman
-Lucio2
-Baptist
Baptiste in the back row: “Baps in the back“
Baptiste in the junkrat trap: “ Baps in the trap”
I would say just the regular name, but the pt sound in the middle would be cumbersome in a match. Not smooth like ‘monkey monkey monkey monkey’ XD
Baps I guess? No real stand outs to me.
I’d prefer Lucio1
-Bautista
-Barista
Bappy/Bapty perhaps.
Realistically, just Bap.
Drax the Destroyer
audible grumbling within the forums
Mr. Fortnite or Generic Soldier
Also Fortnite Default Skin works pretty Well for him too. " Hey plz Switch to Fortnite Default Skin "
Bappy Boop? 
I thought the same, but it’s ironic given the p is supposed to be silent.
Bapto-Bismol
Give him the pink skin from spark
Thats perfect. 
It’s a French name… the P isn’t silent.
Ba-tees(t).
Your list failed to include the one and only nicknamed needed:
Amend this, OP.
Bap Tasty
why won’t you die?
You might want to re-listen to those. While they slur the consonants a lot (rightfully so, as it’s accurate to what French speakers do), the sound is definitely in there.
It actually ends up sounding more like a B in natural speech, but it is technically supposed to be a P sound.
Baptise-Church
I actually lol’d. Does that make a racist sexist?
After careful thinking, analysing everyone’s input and heavy considerations, what about…
Baptise