After Benjamin Corgnet cancelled out Anthony Soubervie's late penalty, goalkeeper Stephane Ruffier proved the hero by saving Xavier Mercier's fifth penalty to send his side into the final four.
Following a low-key opening hour, Boulogne led after 80 minutes when Ruffier brought down Soubervie inside the area, allowing the forward to slot home the opener.
The decision seemed somewhat harsh but it mattered little when Corgnet headed home from a corner five minutes from time to take the tie into extra time.
The best chance of the final 30 minutes came when Mevlut Erdinc headed wide from five yards out.
However, the game went to penalties and Loic Perrin and Baidy Dia failed to score in the opening eight spot-kicks.
After Dia's miss, Francois Clerc slotted home to pile the pressure on Mercier, with Ruffier saving to ensure a semi-final berth for the six-time tournament winners.
