I have the La Sportiva FC ECO 4.0 GTX and was wondering if these crampons would work well with this boot, can anyone help me out

Both AC and Albert are correct, those boots aren't the best boots for crampon use, but these crampons will do a great job strapping to them. For what its worth, my winter hiking boots are not made for mountaineering, and because they don't have a shank they are very flexible. I have taken my boots with these crampons up slopes greater than 45 degrees with no problems, it's just a little more work for the calves.

Also you might want to consider getting the flexable connector bars if your boots are pretty flexable. Walking in flexable boots with the regular connector bars hurts your feet.

Those boots aren't going to be be great for crampon use. They are very flexable and will not be very secure gonig up anything even a little steep. Also they won't be the best on softer snow slopes that you might want to kick steps in. But for basic walking around on a low angle glacier or frozen snow field, these will be perfect. Just make sure and get the "strap" version which will work with just about any footwear from sneakers to double plastic boots.