How to mount a narrow component on breadboard?
Use 2 straight pin headers and bend one (or both) and solder the relay on top of it (left picture).
Place the headers in the breadboard, bend the pins, solder the first pin and the last of the header to the relay. 

Or use a straight header and a right-angled SMD header (like the SL 1X10W SMD2,54 ) (right picture).
The displacement of the pin at the top to the bottom pin is about 1.7 mm, so it would fit almost perfectly (2*2.54mm - 1.7 mm =  3.4 mm). Because you probably solder the pins not heart on heart, but next to each other, you will manage to bridge the remaining 0.2 mm.

To prevent breaking the solder joints, make sure when removing the relay from the breadboard to not hold and pull on the relay itself, but to hold and pull the pin headers.
Or use something like hot glue to fixate the header to the relay.