Trinity raced into a 22-0 lead through Johnstone, Jacob Miller and Craig Hall, but Gavin Marguerite and Mourad Kriouache reduced the score to 22-10.
Matty Ashurst extended the lead after the break but Danny Hulme and Kuni Minga tries had Wakefield wobbling.
However, Johnstone added another two scores to see off the League One side.
Wakefield head coach Chris Chester:
"Toulouse are a good football side and scoring four tries in those first 15 minutes is probably the worst thing that could have happened to us.
"We seemed to score with ease but our completion rate in the second half was only 43 per cent and we did a hell of a lot of defending.
"But fair play to Toulouse, they threw the ball around well and caused us a lot of problems.
"I was just disappointed with our attitude, line speed and our short-side defence. We need to be better and if that had been a Super League side, I reckon they would have turned us over today."
Toulouse head coach Sylvain Houles:
"The boys are actually disappointed because they could have come away with a win. We had plenty of opportunities and our attack was pretty good.
"It was very encouraging for us and we need to get out of League One now and into the Championship."
Wakefield: Jowitt; Jones-Bishop, Walton, Hall, Johnstone; Miller, Finn; England, Howarth, Arona, Kirmond, Ashurst, Sio.
Replacements: Simon, Crowther, Yates, Anderson.
Toulouse: Kheirallah; Maurel, Marguerite, White, Minga; Ford, Hulme; Boyer, K. Bentley, Canet, Planas, Curran, Marion.
Replacements: Kriouache, Puech, Masselot, Hepi.
Referee: Chris Kendall
Tom Johnstone's four tries helped Wakefield into the Challenge Cup quarter-finals for the first time since 2008 with victory against Toulouse.