Ah the wonderful world of tire sizes, where nothing is what it seems! There are multiple size systems (French, fractional, decimal, ISO), and only ISO/ETRTO, the "international standard" is (somewhat) consistent. Unfortunately, many people don't use the ISO/ETRTO system.
The definitive guide to tire sizes is Sheldon Browns' site:
The only thing I would like to add to the mighty Sheldon:
Avoid any tire with fractional markings (such as 26 x 1 1/4) like the plague, unless you are 100% sure what you are doing.
On to your question:
Your current tire: 26 x 2.0
This one of the most common MTB sizes, measured in inches:
26 in. diameter, 2.0 in. width.
Equivalent ISO = 599mm (diameter) x 50mm (approx. width)
Your new Btwin tire: 700 x25c
700 is a French size often used for road/racing cycles. Since the French like their millimetres, a 700 x 25 means "700" diameter, 25mm width. To complicate things, the French "700" is not the same as the ISO diameter...
Equivalent ISO = 622mm (diameter) x 25mm (width).
Since the diameters are not the same, your new tire will not fit. There is also a large difference in tire width (50mm for the old tire, 25 for the new)
General tire selection advice:
1) Get the ISO diameter size right first. This is the only measure that can be somewhat relied upon.
2) Check tire width & rim compatibility.
Get the diameter size right first, then check the tire width. Small/skinny tires will not fit on very wide MTB rims. Fat tires will not fit on narrow rims. Measure your rim width. Sheldon Brown's site has a table that shows rim width vs. tire width compatibility.
From personal experience, I have established these quick and dirty rules regarding tire width:
Racing cycle wheels: 23mm - 30mm (but the wider tires probably will rub the frame)
City bike wheels: 30mm - 47mm
MTB wheels: 35mm- 60mm