BAGHDAD—Several Middle Eastern leaders and French President Emmanuel Macron met in Baghdad on Saturday at a summit hosted by Iraq, which wants its neighbors to talk to each other instead of settling scores on its territory. Relationships within the region are strained chiefly by hostility between Iran on one side and the United States and its Arab Gulf allies on the other. Organizers said they did not expect any diplomatic breakthroughs at the summit. “Getting these countries to sit around the table—that will be achievement enough,” said one Iraqi government official. Heads of state attending included President Abdel Fattah al-Sisi, King Abdullah of Jordan, Qatari Emir Sheikh Tamim bin Hamad al-Thani and Macron. Kuwait and the United Arab Emirates sent their heads of government, and Turkey its foreign minister. Macron’s trip to Iraq over two days aimed to support the regional dialogue, meet Iraqi political leaders and visit French special …