Why Not Frame It Out And Fill It
The usual approach is a stud wall against the foundation with batt in it and poly over the front.
That puts an absorbent material tight against damp masonry, with a cavity behind it holding air. In winter, indoor moisture reaches the cold concrete through every gap in the poly. In a foggy summer, humid air gets in there and has nowhere to go.
The result is a cavity that stays damp, and everything that follows from that.
Closed Cell Straight Onto The Wall
Foam goes directly onto the masonry. No cavity, nothing absorbent, nothing for moist air to occupy.
At sufficient thickness closed cell is its own vapour control, so no separate poly layer is needed and none should be added. Adding one traps moisture between two barriers.
The wall behind can stay as damp as it likes. Nothing on the warm side of the foam can take on water, because there is no water-absorbing material there to take it on.
Studding can go on afterwards for finishing, on the warm face of the foam, where it stays dry.
The Header Is Half The Job
Where the joists land on the foundation there is a band of framing running the whole perimeter. It is thin, exposed to outside on one face, and jointed top and bottom.
In most older buildings it holds a scrap of batt and a lot of air. It is one of the biggest leaks in the building and one of the smallest areas to treat.
The provincial rebate schedule recognises this and pays between roughly $1.00 and $3.00 a square foot for header insulation, which is a higher rate than the walls themselves. Basement and crawl space walls pay around $1.00 to $2.00 a square foot depending on the R-value added.
Cold floors on the ground storey are very often this and nothing else.
What The Space Becomes
Once the walls and the header are sealed, a cellar stops being a separate climate. It comes within a few degrees of the rest of the house on its own.
The seasonal smell goes, because the air exchange driving it has stopped.
The floor above stops being cold, which is usually the thing that prompted the call in the first place.
Foam has to be covered in occupied space. Half inch gypsum board is the standard assembly, and we tell you at quoting stage whether that sits in our scope or yours.