It wasn't quite winning ugly, but Wales once more showed the skill that often separates good teams from the rest – getting a result when not at your best.

The win that clinched Championship and Grand Slam, in both cases a third in eight seasons, was much more grind than flourish. But then so, for all the praise heaped upon them, was most of their season.

Wales coach Warren Gatland said that his feeling at the end was "relief as much as anything, rather than jubilation". He praised his group of players, saying "[They are] a credit to themselves, to Wales and to Welsh rugby. They're excellent professionals and make our job very easy as coaches, because they always do more than is expected of them."

They could never quite shake off a limited but highly determined French team, and had they lost might have pointed with serious regret to the two first-half penalties that struck the posts but bounced back rather than crossing the bar. But it did not ever really look as though any other result was likely.

Only once did the day's chief storyline seem likely to alter and that came 10 minutes from time when the umpteenth towering up-and-under from French outside-half Lionel Beauxis for once failed to find a Welsh catcher, requiring desperate covering and tackling to keep the visitors at bay. It was a tough, attritional contest whose flow was constantly broken by Craig Joubert's persistent penalising of the attacking team at the breakdown. But as is so often the case, it was a turnover that produced the decisive moment.

Midway through the first half, with France leading 3-0, Wales lock Alan-Wyn Jones stole possession in French territory. Outside-half Rhys Priestland passed flat and hard to giant wing Alec Cuthbert who showed that he is much more than a large, blunt weapon by cutting sharply inside to wrong-foot French flanker Julien Bonnaire and, running a superb line, charge 40 metres untouched to score. It was Wales's 10th try of the tournament, every one of them scored by their three-quarters and full-back, and Cuthbert's third. Leigh Halfpenny landed the conversion and Wales, leading 7-3, were never again caught. By half time it was 10-3, with Halfpenny landing a penalty after lock Ian Evans had charged down a French clearance.

Wales skipper Sam Warburton was forced off with an injury at half time and like his 2005 predecessor Gareth Thomas, will go into the record books as a Grand Slam captain having played two-and-a-half of the five matches.

His replacement was the 2008 leader Ryan Jones, wearing a headband which in turn offered an echo of the late Mervyn Davies, the 1976 Grand Slam captain, whose death last week was marked by the team's black armbands and a pre-match silence.

The second half was still more grinding than the first. Twice France fought their way back to within four points – and on the first occasion, early in the half, Beauxis might have reduced it to a single point had he been on target with a drop-goal attempt. Each time, though, Wales were able to come up with a reply.

However, the mood was still apprehensive until Halfpenny landed his final score with five minutes left. Only then did the roars of the crowd express certainty, and Wales were still wary enough to end the match by simply holding possession.

However, their defence coach Rob Howley, a great player who never won a Grand Slam, said his players "deserve everything they have achieved" and warned that "they can get better over the next four years".

Wales: L Halfpenny; A Cuthbert, J Davies, J Roberts, G North; R Priestland, M Phillips; G Jenkins, M Rees, A Jones; A-W Jones, I Evans; D Lydiate, T Faletau, S Warburton (cap). Replacements: R Jones for Warburton 40, S Williams for Davies (blood54-9), K Owens for Rees 62, L Williams for Phillips 62, L Charteris for A-W Jones 62.

France: C Poitrenaud; W Fofana, A Rougerie, F Fritz, A Palisson; L Beauxis, D Yachvili; J-B Poux, W Servat, D Attoub; P Pape, Y Maestri; T Dusautoir (cap), I Harinordoquy, J Bonnaire. Replacements: J-M Buttin for Poitrenaud 36, D Szarzewski for Servat 44, V Debaty for Poux 44, F Trinh-Dic for Palisson 54, L Picamoles for Bonnaire 59, J Pierre for Pape 67,

M Parra for Beauxis 72

Referee: C Joubert (France)