Difficulties of I2C over wire
You definitely need external pull-up resistors. The internal pull-ups of a microcontroller are too weak. Note that with a high capacitance bus it's usually not a problem to have fast falling edges, because the FETs which pull the line low have low impedance, and then the wire's capacitance can be discharged quickly.   

But for the rising edge we only have the relative high resistance of the pull-ups, and the RC time of that combined with the wire's capacitance determines the rise time. A smaller resistance value is better, but there's a limit to this too: an I2C device doesn't have to draw more than 3 mA, so at 5 V bus voltage the resistance shouldn't be lower than 1.7 k&Omega;.



The graph shows the maximum pull-up resistance for a given wire capacitance. At 1 m that capacitance won't be high, if you use signal wire probably less than 50 pF, and even for 100 pF you could go up to 12 k&Omega;. I'd stay near the lower limit though, not only will you have faster edges, but a lower impedance also makes the wire less sensitive to noise. 2.2 k&Omega; resistors will probably do.  

Further reading
I2C Specification
I2C termination versus capacitance