Combine 1/2 cup flour and salt in a resealable plastic bag. Add chicken to the bag, several pieces at a time, and shake to coat completely.
Heat a sauté pan over medium-high heat, and add butter and oil. Place chicken in pan and cook for 8 to 10 minutes, turning once, until browned on both sides. Using tongs, transfer chicken to paper towels to drain, then arrange pieces in the slow cooker.
Set the sauté pan over medium-high heat and add onion. Sauté, stirring frequently, for 10 minutes, or until lightly browned. Sprinkle with remaining flour, and cook until browned. Gradually add wine, stirring to scrape up browned bits from the bottom of the pan. Add stock and cook, stirring frequently, for 10 to 15 minutes, until sauce is thick enough to coat the back of a spoon. Pour sauce over chicken in slow cooker and lay 2 sprigs of tarragon on top.
Cover and cook on low until chicken is tender, at least 3 hours (up to 8 hours). At 3 to 4 hours, chicken will still be firm and hold its shape. At 6 to 8 hours, the meat will be falling off the bone.
Pour in cream and stir well. Cover and cook 10 to 15 minutes to heat thoroughly. While chicken finishes cooking, strip leaves from remaining tarragon sprigs and coarsely chop. Remove and discard tarragon sprigs from slow cooker and stir in freshly chopped leaves.
Turn off slow cooker. Divide chicken and sauce among plates; serve immediately.
Try another Crock-Pot recipe: Indian Lamb and Spinach Curry
Adapted from The Gourmet Slow Cooker, by Lynn Alley, copyright © 2003 (with permission from Ten Speed Press).