###NOTE: This is a work in progress... I'm still working on a solution

You are probably getting this error, because you have placed the files L3G.cpp and L3G.h in a folder called IMU in the same folder as your .ino file. This causes the undefined error, as, while the IDE sees the declaration in the L3G.h file, the IDE can not find the definition in the L3G.cpp file.

This is easy to resolve.

If you download the l3g-arduino-master.zip file from https://github.com/pololu/l3g-arduino, and from within the Arduino IDE you then add the zipped up L3G library to the Arduino library, using Sketch ► Include Library ► Add. ZIP Library... and then change the line

#include "IMU/L3G.h"

to

#include <L3G.h>

Then it should compile and link without a problem

As Juraj rightly points out, you have a typo, which should give you the following compile time error:

In file included from sketch/Sensor.cpp:1:0:
Sensor.h:17: error: 'pivate' does not name a type
 pivate:
 ^

Here is the correct code for Sensor.h

#ifndef Sensor_h
#define Sensor_h

#include <EEPROM.h>
#include "IMU/L3G.h"

#define CUTOFF_FREQ 30
#define FREQ 400


class Sensor {
public:
    Sensor();
    ~Sensor();    
    void Init(void);

private:
    L3G gyro;
};
#endif

As Juraj rightly points out, you have a typo, which should give you the following compile time error:

In file included from sketch/Sensor.cpp:1:0:
Sensor.h:17: error: 'pivate' does not name a type
 pivate:
 ^

Here is the correct code for Sensor.h

#ifndef Sensor_h
#define Sensor_h

#include <EEPROM.h>
#include "IMU/L3G.h"

#define CUTOFF_FREQ 30
#define FREQ 400


class Sensor {
public:
    Sensor();
    ~Sensor();    
    void Init(void);

private:
    L3G gyro;
};
#endif

Using Arduino IDE 1.8.5 with Teensyduino 1.42 with:

• https://github.com/pololu/l3g-arduino
• https://github.com/nox771/i2c_t3

However, once the typo has been corrected, as above, then I too can reproduce your problem (sort of), with these link errors:

/var/folders/kp/xv3y9k114yq2_64pf8zwh76h0000gp/T/arduino_build_136680/sketch/Sensor.cpp.o: In function `Sensor::Sensor()':
/var/folders/kp/xv3y9k114yq2_64pf8zwh76h0000gp/T/arduino_build_136680/sketch/Sensor.cpp:3: undefined reference to `L3G::L3G()'
/var/folders/kp/xv3y9k114yq2_64pf8zwh76h0000gp/T/arduino_build_136680/sketch/Sensor.cpp.o: In function `Sensor::Init()':
/var/folders/kp/xv3y9k114yq2_64pf8zwh76h0000gp/T/arduino_build_136680/sketch/Sensor.cpp:14: undefined reference to `L3G::init(L3G::deviceType, L3G::sa0State)'
/var/folders/kp/xv3y9k114yq2_64pf8zwh76h0000gp/T/arduino_build_136680/sketch/Sensor.cpp:19: undefined reference to `L3G::enableDefault()'
/var/folders/kp/xv3y9k114yq2_64pf8zwh76h0000gp/T/arduino_build_136680/core/core.a(main.cpp.o): In function `main':
/Volumes/Home/Users/user/Local_Apps/Arduino/Arduino1.8.5-Teensy.app/Contents/Java/hardware/teensy/avr/cores/teensy3/main.cpp:53: undefined reference to `loop'
collect2: error: ld returned 1 exit status
Multiple libraries were found for "Servo.h"
 Used: /Volumes/Home/Users/user/Local_Apps/Arduino/Arduino1.8.5-Teensy.app/Contents/Java/hardware/teensy/avr/libraries/Servo
 Not used: /Volumes/Home/Users/user/Local_Apps/Arduino/Arduino1.8.5-Teensy.app/Contents/Java/libraries/Servo
Error compiling for board Teensy 3.5.

###NOTE: This is a work in progress... I'm still working on a solution