It is possible to use the two fabrics. When preparing the strips sets I would make one of the fabrics wider than the other , to give a bit more visual interest.
The fence rail pattern is one of the simplest patterns to adapt.
all you need to do is fugure out the size of the block you want to work with. An easy way to do it is measure the finished strip set in the width, and cut the strip sets the same measurement. So if you have two fabrics to get to a 6 inch unfinshed block one fabric cut would be 3 1/4 wide and the other would be 3- 1/4wide. This strip set would be 6 inches ( and the blocks cut from the strip sets would be 6 inches ( for a 5 1/2inch finished).
You can make any combination of widths of the strips work, you just have to cut the blocks from the joined strip set that same width to make the square.
The "rail" in the block is fabric that "connects" to the same fabric, by repositioning the block so the "rail" fabric is vertical , then in the next it is horizontal,repeating these same positions across the row. The next row would start with with the opposite of the first row . So if you started the first row with a horizontal , the second row should start with a verical block.
I added a sketch of what it would look like