I think finding a sub for the butter and cream in the recipe will be a challenge. The sauce is butter fat and vinegar rich. Subs that I would typically use for cream-like coconut oil and coconut milk will likely not work here because of the traditional french flavors and the red wine vinegar. Lactaid may work, but it probably doesn't have the fat content of heavy cream to enrich the sauce.

I presume that you and your family are lactose-intolerant to the point that taking an enzyme doesn't help? Here's an idea that just might work - I've tried this in cream pies and it works divinely, but cooking it into a French-style dish might be a different story. You'll still get a delicious dish, but I can't guarantee the texture. Get a block of good-quality silken tofu and drain it as well as you can (there are internet tips you can look up for that). Whip it with an electric mixer or in a blender until it's creamy and fluffy and light - the denser it is, the closer to the original amount of cream you should use (if it's fluffy and light, you might want to add more). Good luck. Let me know if it works!

I think TLD might be onto something here. If you try the tofu please let me know how you like it. Be sure you really do reduce the vinegar down to a syrup of just a few tablespoons before adding the tofu.