Wales head coach Wayne Pivac has called Gareth Davies and Ross Moriarty into the starting line-up for Saturday's Guinness Six Nations clash against France.
Pivac has made two changes from the side beaten by Ireland 12 days ago.
Prolific try-scorer Adams took a knock to his hip, while Biggar failed a head injury assessment.
Northampton star Biggar suffered two head injuries during the World Cup earlier this season.
He has fully trained since last week and completed all return-to-play protocols.
All testing was undertaken with the addition of a globally-renowned concussion expert reviewing Biggar's return, which was proactively sought by the Welsh Rugby Union's medical team.
Williams and Wainwright are both among the replacements, where there is also a role for uncapped Wasps lock Will Rowlands.
Pivac said: "Gareth was unavailable in round one and came off the bench last time out, so he is full of energy and we are looking forward to him bringing his game on Saturday.
"Ross has impressed off the bench so far and brought a lot of energy and communication as well, so he deserves an opportunity to start.
"We have changed around the second-rows on the bench. We are looking at creating competition there, and Will has trained well and we are looking forward to seeing him out on that stage.
"We want to build on what we have done so far and are looking to be more accurate with what we do and improve on that aspect.
"Saturday is going to be a packed Principality Stadium, we know the atmosphere will be electric, and it is set for a big day in Cardiff."
Victory for Wales would keep them in the Six Nations title mix – and recent history is on their side.
France have not won a Six Nations game in Cardiff since they triumphed there 26-20, 10 years ago, losing on four successive occasions.
Wales have also won eight of the countries' last nine meetings, including a World Cup quarter-final in Japan four months ago.