The 25-year-old, whose place in the starting XV will be taken by Scott Lawson, was viewed as a weak link in the team which stunned the French in the 20-16 win at Murrayfield on Sunday.
Hadden said: "This was an incredibly tough decision. It is not all about the hooker, we are happy with his performance."
Wales had to deal with a player "sit-in" protest yesterday when Gavin Henson's controversial book returned to haunt the team - resulting in their demanding its author leave the team press conference. The players refused to speak to the media until BBC journalist Graham Thomas, who ghosted Henson's book, My Grand Slam Year, left the room.
How the sides will line up at the Millennium Stadium on Sunday:
G Thomas (capt, Toulouse); M Jones (Llanelli Scarlets), H Luscombe (Newport-Gwent Dragons), M Watkins (Scarlets), S Williams (Ospreys); S Jones (Clermont Auvergne), D Peel (Scarlets); D Jones (Ospreys), R Thomas (Cardiff Blues), A R Jones (Ospreys), I Gough (Dragons), R Sidoli (Blues), C Charvis (Newcastle), M Williams (Blues), M Owen (Dragons). Replacements: M Davies (Gloucester), G Jenkins (Blues), G Delve (Bath), A M Jones (Scarlets), M Phillips (Blues), N Robinson (Blues), L Byrne (Scarlets).
H Southwell (Edinburgh); C Paterson (Edinburgh), M Di Rollo (Edinburgh), A Henderson (Glasgow), S Lamont (Northampton); D Parks (Glasgow), M Blair (Edinburgh); G Kerr (Leeds), S Lawson (Glasgow), B Douglas (Borders), A Kellock (Edinburgh), S Murray (Edinburgh), J White (capt, Sale), S Taylor (Edinburgh), A Hogg (Edinburgh). Replacements: R Ford (Border), C Smith (Edinburgh), S MacLeod (Border), J Petrie (Glasgow), C Cusiter (Border), G Ross (Leeds), S Webster (Edinburgh).Reuse content