FlyingOink - is that a male fantasy, the notion of "arrangements" that the wife knows about but that is never discussed? Sounds like a lot of resentment and tension in real life, and I've never knowingly seen it happen.
I have no idea how often this happens, I doubt very often, but I can cite examples from within my wider family and family friends of my parent's generation (born between WW1 and WW2) where there was definitely no resentment or tension as a result.
One example would be of one of my aunts and her husband, who were childhood sweethearts, married young and remained very happily married until her death in her 60's. They had one son but her husband also had a daughter with her best friend, who was married and also had several other children with her own husband.
(Note: there was eventually huge "resentment and tension as a result" in the best friend's marriage but that was due to a husband's reaction rather than a wife's.)
The circumstances were unusual. My aunt had a very debilitating, painful chronic illness that started in her 30's and eventually killed her. Who knows what their sex life, if any, would have been like if she had been well. As it was, she was much too ill most of the time to be at all interested.
Her husband worked full-time in heavy industry and shared the housekeeping and cooking with their son. The son was always in full-time employment, was as much of a "homemaker" as his parents, was happy to stay living in the family home but had a very full life including a long-standing relationship with a woman who did not want children and wanted to live alone.
My aunt and her husband were a lively, happy, sociable couple and there was a close-knit, supportive family unit with my male cousin.
I do not know how my aunt became aware of her husband's affair or if they ever discussed it. She and her best friend tacitly acknowledged it and my aunt was delighted when her best friend told her "in passing" that she was pregnant, my aunt knitted baby clothes for her, etc. and it was understood between them who the father was. (Those were the days before The Pill, when an unplanned pregnancy was a much likelier consequence of an affair.)
The affair lasted many years and only ended when the best friend's husband found out and threatened to kill her. He never suspected the parentage of her youngest child.
My understanding is that the best friend's husband was never a kind or pleasant man and that my aunt was very happy with an "arrangement" that brought happiness to both her husband and her best friend.
My aunt lived on the other side of the country and I know most of this because she and my mother spent at least an hour on the phone to each other every Sunday.
The affair and the parentage of my cousin's half-sister became something of an "open secret" in later years. The best friend died before my aunt and her husband. After my aunt died, her husband never recovered from the loss. Despite being fit and healthy he died less than two years later. My cousin said that the GP told him that he had essentially "died of a broken heart".
I didn't know if my cousin was aware of the existence of his half-sister until his father's funeral, when he introduced me to his half-sister. They explained that they had each known about the other since their late teens, had sought each other out in their twenties and had been friends since then. It was a particularly important friendship for my cousin because he was an only-child.
I think my cousin was about 8 years older than his half-sister. It is a small town and their mothers were worried about the possibility of inadvertent incest so they each told the children when they were old enough to understand.
As far as I am aware, their blood-relationship is still a secret except on a "need to know" basis. Some but not all of the half-sister's siblings were aware of it. Another cousin is aware of it and she finds the whole thing repulsive and reprehensible.
My cousin died childless in his 50's, I met his half-sister again at his funeral and some of these details I learned from her.
Those circumstances are unusual but the pre-existing friendship between "the wife and the mistress" and the fact that there was never any intention to end either marriage seem at least as significant as my aunt's illness and her husband's actions in seeking sex elsewhere. His "male desire" is just part of a bigger story.
The other examples I could cite are all rather different.
Some involve friends of my mother who remained in unhappy marriages to mostly rather horrible men "for the sake of the children", wives who were more than happy for their husbands to be getting their jollies elsewhere rather than using them for sex and raping them.
Others relate more to the other quote below . . .
Is it like the mythical Frenchman and his mistress? Or is it just a fantasy that a man can have a woman on the side without any difficult conversations at any point?
Is it a myth? It is interesting that this is always framed in this way. Why not, "Is it like the mythical Frenchwoman and her lover? Or is it just a fantasy that a woman can have a man on the side without any difficult conversations at any point?"
The other examples I could give are relationships where both parties have had or are having affairs, sometimes very long-standing, and there is a mutual wish to avoid those "difficult conversations".
They would include "live examples" of those sorts of relationships happening right now.
Personally, I would find that sort of relationship very uncomfortable. Being "the other woman" is a doddle by comparison, although it is something I have generally tried to avoid.