General de Piepape wrote a biography of the Duchesse du Maine in 1910, which was translated in 1911 into English, and has pretty much the same thing to say as W H Lewis about Mlle du Maine: "She lived withdrawn in a corner of the palace [Sceaux], caring little for society or intellectual pursuits, and taking, apparently, a view of life diametrically opposed to her mother's. History has nothing of note to record of her."
However, he does make a few observations here and there; in 1717 the three du Maine children were introduced to Made de Maintenon, effectively their grandmother by affection if not by blood, and she wrote that "Monsieur du Maine wanted me to see them. They called here yesterday on their way back from Rambouillet [the chateau of their uncle, the Comte de Toulouse]. They are everything that one could wish; they spoke just as they ought to at their age - there was not a word I should have added or left out, and their grandfather [Louis XIV] would have been highly pleased with them. " It appears that Mlle du Maine was placed in 'L'abbaye Notre-Dame-la-Royale dite Maubuisson', a very superior convent although from what age Piepape does not say. When the du Maines were arrested for their part in the Cellamare conspiracy, she was "reinstalled at Maubuisson" as if perhaps she were elsewhere at the time - whether with one or other of her parents (they were arrested separately, in different locations) is not said. Madame du Maine was imprisoned in various fortresses, but eventually was moved to the more salubrious Chateau de Savigny-sous-Beaune in 1719, at which stage she begged that her daughter might be sent to Anet where her grandmother the Princess de Conde was anxious to have her. However, Mlle du Maine was transferred from Maubuisson to another convent at Chaillot where she stayed until about 1720, when her recently-released father took her and her brothers with him to Sceaux for a very lukewarm (on his part) reunion with their mother.
When the Duc du Maine died in 1736, Louis XV granted a pension to the Duchesse and Mlle du Maine, so they were not at all badly off. As W H Lewis observed, Mlle du Maine inherited the Duc's appartments at Versailles. Piepape writes that the marriage negotiations with the Duc de Guise apparently occurred in 1739, when she was 32; the Duc de Guise was 18. However, what ended the discussions was not the disparity of age, but money, as the Duchesse du Maine stipulated that the Duc should contribute a revenue of 50,000 livres which the Duc was apparently unwilling to pay. However, I am dubious about this Duc de Guise; the title at the time was invested in the House of Conde and the Duc de Guise in 1739 was not 18, but 3, the son of the Prince de Conde and Louise Francoise's first cousin. Piepape also alleges that in 1740 there had been some talk of marrying Mlle du Maine to the Prince de Monaco, who was 51 and a widower, which sounds a little more likely; however, it didn't come to anything either.
Piepape has one further anecdote about Mlle du Maine; her court hoops were so large that on one occasion they became entangled with those of the Queen and the two women had to stand and pull against each other to disentagle themselves. Louis XV was most annoyed and M. de La Tremoille was sent to the Duchesse du Maine with the measurement for the hoops Mlle should wear, with the rider that in future she should stand at a more respectful distance from the Queen. Piepape suggests that Louise Francoise only wore such ultra-fashionable clothes at the instigation of her mother, but he shows no evidence to support this. He adds that "she was neither pretty or attractive, and save for her dowry, no one would have sought her hand" - I don't know on what basis he made those remarks, but since beauty or wit or charm was generally noted in the princesses of the blood, it seems likely that no mention means there was nothing to note.
Louise Francoise was "taken ill while out riding" noted the Duc de Luynes in his diary. "No sooner was she place in her carriage than she fainted away. She never recovered consciousness, and died a few hours later". She was buried in the Church [chapel?] at Anet where her remains were undisturbed by the Revolution - she was too obscure to excite interest, poor woman.