Well, according to Wiki (never heard of the guy before, no time to find better sources), Heinrich was humble and open, was a good diplomat, pragmatic, as well as a proponent of submarines and airplanes.
If we take this to the logical extreme, foreign policy under Henry I would be more mild than OTL under Wilhelm. Maybe Bismarck will stick around longer... and the various crises of the late 19th-early 20th century will be handled less militarily and more diplomatically. I suppose we could throw in a brand-spanking-new Kaiserliche Marine and Luftstreitkräfte for good measure.