Is a marriage based on love invalid, in reliance upon the legal maxim, "That which is built upon falsehood is false"?

Common relationships between young men and women in the name of love are not sanctioned by Islamic law; they are a gateway to temptation and corruption. However, if a man loves a woman without actively pursuing the means to it, there is no harm in that, as long as it does not lead to something forbidden or prevent him from an obligation. Marriage is the optimal path and the effective remedy for this attachment, as the Messenger of Allah, peace and blessings be upon him, said: "We have not seen for two who love one another anything like marriage." Marriage after a forbidden love relationship is not invalid, because it is not based on the forbidden relationship, but on its lawful pillars and conditions.