I finally found the solution thanks to this post.
The problem comes from the fact that Mavericks has changed the way apps are signed. Every framework embedded in an app should be signed as well now.
To do so, I just added a "Run Script" Build Phase with those lines:
LOCATION="${BUILT_PRODUCTS_DIR}"/"${FRAMEWORKS_FOLDER_PATH}"
IDENTITY="Developer ID"
codesign --verbose --force --sign "$IDENTITY" "$LOCATION/Sparkle.framework"
codesign --verbose --force --sign "$IDENTITY" "$LOCATION/../XPCServices/com.andymatuschak.Sparkle.SandboxService.xpc"