The Infraction Procedure GuideInfraction Procedure Guide is the wrong document to refer to at FNM. FNMs are run at Regular REL, where players generally do not get penalized for gameplay errors. See the Judging at Regular REL document for the kinds of fixes (rather than penalties) that can get dispensed at FNM. In this case, after you notice 7 cards in what should be your hand of 6, just shuffle one back. If you don't like your hand, you can continue taking mulligans normally.
From the section on drawing extra cards:
If the identity of the card(s) were known to all players, return them to their proper location. Otherwise, determine how many extra cards have been drawn, take that many cards at random from the player’s hand and place them on top of the library. Don’t shuffle the library after doing this! If the extra cards were drawn while drawing an opening hand, shuffle the extra cards back into the deck instead and allow the player to continue making mulligan decisions with the remaining cards.
If you were playing at a Competitive REL tournament, you would receive a Game Play Error warning, and you (the player who took an incorrect mulligan) would have the option of two fixes: you could simply take an additional mulligan and go down another card, or you could reveal your hand and let your opponent choose cards to be shuffled back until you're down to the correct number of cards for the initially incorrect mulligan. So if you had mulled to 6 and drawn 7, in the second option you would let your opponent choose which single card to be shuffled back.
Of course, when in doubt, always call a judge.