VERDUN, France — In solemn ceremonies here Sunday, French President Francois Hollande and German Chancellor Angela Merkel marked 100 years since the Battle of Verdun, determined to show that, despite the bloodbath of World War I, their countries’ improbable friendship is now a source of hope for today’s fractured Europe. The 10-month battle at Verdun – the longest in World War I – killed 163,000 French and 143,000 German soldiers and wounded hundreds of thousands of others. Between February and December 1916, an estimated 60 million shells were fired and one out of four didn’t explode, making the area so dangerous that housing and farming are still forbidden.