Francis was a realist, from what I have read of him. He knew Madeleine was sickly and likely wouldn't have a long life. But her father, like any father, wanted her to live as long as she could. She spent her earlier years with her Aunt Marguerite. While her health was always delicate, it wasn't until years later when she was brought back to Paris to live with her stepmother, that she contracted TB. She did only short months before her wedding was celebrated.
He refused the marriage numerous times, not wishing to send her. But Madeleine convinced him to let her. And while he likely did find some comfort that his beloved favorite child had found happiness for a short time, there was likely also guilt. Even guilt before he sent her to Scotland, wondering if he had simply left her with her aunt in Loire, would she have ever contacted TB. She may have been delicate, but she may have lived a longer life.