Peel pears, halve lengthwise (leaving stems on half of pieces), and core.
Put pears in a 5- to 6-qt. pot. Add wine and sugar. Scrape seeds from vanilla pod into pot, then add pod and water to barely cover pears (3 to 4 1/2 cups).
Cover and bring to a simmer over medium heat; then reduce heat and simmer gently, stirring occasionally, until pears are as soft as butter when pierced with a knife, 30 minutes.
With a slotted spoon, transfer pears from pot to a large, wide bowl. Boil syrup, uncovered, over medium-high heat until reduced to 2 cups, 30 to 35 minutes; reduce heat if pan starts to scorch. Pour syrup over pears.
Spoon 1/4 cup crème fraîche into each dessert bowl and add a pear half to each. Stir syrup and drizzle over pears. Tuck in rose geranium leaves.
Make ahead: Through step 4, up to 1 day, chilled airtight.