Les Bleus will meet Wales next Saturday in Auckland after taking advantage of a shambolic showing by England.
First-half tries from Vincent Clerc and Maxime Medard propelled France, apparently in disarray following last week's loss to Tonga, into a 16-0 lead.
Ben Foden responded with a touchdown in a better second half for England but France edged further ahead with a drop goal from Francois Trinh-Duc.
And although Mark Cueto wrestled his way over the line for a try in the closing minutes, England limped out of the tournament as France advanced to the last four.
Following a turbulent week, Lievremont expressed satisfaction that France's tournament remained on track.
Lievremont said: "I'm extremely proud, very happy. It's a beautiful end of the week.
"The whole week has been very exhilarating, I have to say. Many beautiful things have happened and I'm delighted."
Lievremont had faced criticism following the defeat to Tonga, but he did not consider the remarkable rise in performance as vindication.
He added: "I have promised to myself that I wouldn't be bitter, sour, so this is just happiness. It's very simply happiness. That's it."
Wales beat Ireland 22-10 in Wellington to advance to the semi-final clash with France.
Lievremont added: "I had already starting watching the matches of our future opponents - Ireland or Wales. Wales are playing very well.
"I would've maybe put my money on Ireland because they seemed more consistent.
"However, Wales have a very good team, a very brave team in the forwards, a lot of talented defence players.
"They control their game very well. It's not going to be easy, but I would like to start thinking about it already now.
"I'm going to encourage my players to celebrate this win, but I'm going to encourage them to start focusing on the semi-final as quickly as possible."
France captain Thierry Dusautoir was immense as part of a phenomenal effort as his side demonstrated a spirit that was missing earlier in the tournament.
Dusautoir said: "I think most of us realised that we were missing out on an extraordinary opportunity to be here, to play in a World Cup for our country.
"This is quite unique. It's the kind of experience you have maybe only once in a lifetime.
"I don't know whether today we played something extraordinary or beautiful rugby, but we had 22 French players who really wanted to go on in this competition.
"Today we have qualified for the semi-final. That's wonderful. However, now we have to get ready for the semi-final.
"But, we are obviously happier than last week."
Four years ago France defeated favourites New Zealand in the last eight before losing to England in the semi-final.
Dusautoir hopes his side can put in another strong performance at Eden Park next weekend and go through to the final.
The flanker added: "We want to win next week as well so we have to start working very quickly. We have to refocus for this new game against Wales.
"The situation is very different (to 2007) but the feeling is just as intense because we are qualified for the semi-finals.
"We might not have won against the best team in the world this time, as was the case in 2007 against the All Blacks. However, we have shown that we can play differently from what we have done so far.
"We showed that we could play rugby, good rugby and really be proud of the team."
Gilbert has released a new line of rugby cleats. The Gilbert Virtuo 8S is part of the exciting new product. Check it out.
The entire All Blacks apparel line has been updated for 2013/14. Check out the New Zealand All Blacks polo.
The Nike Tiempo is a solid rugby cleat and one of few styles still made from full-grain natural leather.
The Gilbert Blitz 8S rugby cleat is a great cleat at a great price of $69.99. Get a new pair of cleats today.
A cool looking all black rugby cleat with the high performance adidas is known for. Get in the Gear!
Wear the crest of the British and Irish Lions on your t-shirt. A great look for the summer.
The All Blacks Performance t-shirt is black with hints of blue from the training jersey. Very Cool.
The New Zealand All Blacks training jersey for 2013/14. Get in the Gear!
The USA Rugby Pro Alternate rugby jersey is perfect for any fan of the Eagles. Get yours to wear during the summer Test matches.
The NEW All Blacks 2013/14 jersey has arrived at World Rugby Shop. Dare to wear the colors of the All Blacks.