Simple Answer: Is it plausible? Yes
Not so simply answer: yes it is still plausible, but it is probably not going to be practical or cheap:
Practicality for Armour:
As a base metal Tungsten is fantastic as dealing with heat,, but its also very heavy and for its weight it is quite brittle. now turning that into a CMF, would reduce the weight but it won't stop its brittleness being an issue, while it is still metal and strong, it probably won't stop a bullet.
Now when you mix it with steel some of those issues go away, it'll stop a bullet. but the added advantages of Tungsten aren't really there you would reduce the weight loss, but not really add any benefit, and add that compared to steel, tungsten is really really pricey. you adding a lot of extra cost as well
The current price of tungsten is approximately US \$19.85 per pound compared to steel, which is about \$0.45 per pound so it would depend on the ratios used in making the armour.
It would very easily be able to resist Stabs, and arrows, but plain on Steel Metal Foam could do so equally well, (possible a little better) and be lighter
That video appears to be Aluminium or Steel, which are a lot stronger than Tungsten, and while it looks impressive, when you watch slow motion videos of bullets hitting steel plate pretty much the same thing happens
But i had to watch it at work, with the sound off, so if it was spoken saying what it was then please correct me
https://www.youtube.com/watch?v=QfDoQwIAaXg while this video shows materials other than just steel, its a nice video to watch, especially the rifled bullets being peeled apart on impact along the lines of the rifling
the benefits of CMF is its strength compared to its weight.
if it was being designed to go up against energy weapons, plasma laser etc, where the damage done is by imparting heat into the target faster than the target can dissipate that heat then it would be a very very good materiel to use! Tungsten's greatest ability is its extremely high melting point and its ability to dissipate heat.
Edit: Also worth noting, that CMFs are quite advanced armours, and yet going up against swords and spears... are you trying to reform the British Empire?