Short answers, pulled from the story.
Marshal Soult began a counter-offensive in July 1813 that defeated the Allies at the Battle of Maya and the Battle of Roncesvalles. The French lost momentum and were repulsed by the Allies at the Battle of Sorauren on 28 and the 30th of July.
At daylight on the 7th of October 1813, Wellington crossed the Bidassoa in seven columns and attacked the entire French position which stretched from north of the Irun-Bayonne road along mountain spurs to the Great Rhune high. The decisive movement was a passage in strength near Fuenterrabia to the astonishment of the enemy who had thought the crossing impossible at that point due to the width of the river and shifting sands.
During a heavy cannonade on the 10th of November 1813, Wellington attacked this extended position in five columns so directed that after carrying Soult's advanced works a mass of about 50,000 men converged towards the French centre near Amotz. The Allied loss during the Battle of Nivelle was about 2,700 and that of the French 4,000 plus 51 guns.
Wellington decided to attempt bridging below Bayonne where no effort would be expected because the deep sandy soil near its banks made transport of bridging matériel by land laborious and almost certain of discovery. Hope succeeded in passing 600 men across the river in boats on 22 and the 23rd of February before a flotilla of chasse-marées appeared from Saint-Jean-de-Luz on the 24th of February.
On the 13th of April 1814 officers arrived with the announcement to both armies of the capture of Paris and the abdication of Napoleon on the 4th of April. Louis XVIII was restored to the French throne and Napoleon was permitted to reside on the island of Elba sovereignty of which had been conceded to him by allied powers.