MB85RC256V for data logger sensor project?
From what I’ve read of FRAM, writing is more like RAM so you do not have to erase pages before writing, as in flash memories. This is confirmed in looking at the I2C command set and finding no erase commands.

Basically, with one command, you can write sequential bytes to any location in the FRAM. Read/write cycle limits (reads require rewriting so reads must be considered too) are much higher than erase/write cycle limits in flash but are still finite. You could probably get away with always restarting from the beginning but I’d still suggest using the device as a circular buffer so it wears evenly.

Note that this is an I2C device where an SD card is SPI (in the simplest mode). Therefore, it’s not a direct replacement. The interfacing and code is different but still quite doable on an Arduino.