Is 'j'aller' a word in French or is it 'je aller'?

The correct form is "je aller", but this does not appear very often (usually because the "aller" is conjugated to "je vais"). It is worth noting that this is an exception and all conjugated forms of "aller" do take the apostrophe like "j'allais" for "I used to go."

However, a perfect example would be: "Puis-je aller aux toilettes?" meaning "Can I go to bathroom?"