After more than a week of wrangling over the outcome of its hotly contested party election, the leadership of France’s center-right opposition party on Monday confirmed Jean-François Copé, a right-leaning protégé of former president Nicolas Sarkozy, as the party’s new chief, staring down a last-minute legal challenge from his centrist rival, François Fillon. The disputed election has sown confusion and embarrassment across France and in particular within the already bruised party, known as the U.M.P. The drawn-out battle, which has played out on live television and via social media networks, follows Mr. Sarkozy’s loss in the presidential race in May,...