Even at an elementary level, can "force" be defined as "cause of motion"? In Leçons de physique (Lessons On Physics) (auth. Perez, De Boeck editor) can be found this informal definition of force: "forces are what cause motion".
Is this definition accurate?
What I am wondering is whether this explanation of "force" is compatible with the principle of inertia.
I mean, this principle asserts that no force is required for an object to move in a straight line at a constant speed.
Shouldn't it be said that a force is what causes acceleration (i.e. a change in velocity), not motion?
 A: 
"forces are what cause motion"
Is this definition accurate?

The problem here is that you are missing a definition for motion.

Shouldn't it be said that a force is what causes acceleration (i.e. a change in velocity), not motion?

You are right, more clear definition would be that (net) force is what is causing accelerated displacement:
$$\sum_{i} \vec{F}_i = m \Delta \ddot{x}$$
A: Without the complete context, it is difficult to judge the reported expression. However, in a strictly formal sense, and after defining the meaning of some terms, it is correct.
Indeed, if we define motion the time dependence of the dynamical variables  ($\vec r_i(t), \dot {\vec r}_i(t) $), Newton's second law provides a set of second-order ordinary differential equations that, in connection with a starting value of positions and velocities, establishes a causal relationship between the initial values and the values at any subsequent time.
Notice that the special case of zero force is entirely included in this conceptual frame.
A: The second part of the statement shows some questionable logic too.
According to this, it can be understood that forces are the causes of properties like electric charge or gravitational mass. Or maybe I missunderstand his meaning.
Maybe he means that we realize the existence of these properties due to the forces exterted between the objects. I don't live in a French speaking area of the country.
"Les forces sont les causes du mouvement ; ce sont des grandeurs vectorielles notées F qui agissent sur des objets ponctuels en faisant apparaître des caractéristiques physiques telles que la charge électrique, la masse grave, etc."
The forces are the cause of motion; they are vector quantities (labled F) who act on point like objects and causing (or while making to show up) physical properties like electric charge, gravitational mass, etc.
A: 
In Leçons de physique ( Lessons On Physics) ( auth. Perez, De Boeck
editor) can be found this informal definition of force : " forces are
what cause motion".

Personally, I don't like this definition for two reasons.
First, motion does not require a force if the motion is constant velocity.
Second, forces do not necessarily result in a change in motion. Only net forces do that. For example, I can apply a force to a wall in my room without causing it to move (at least, macroscopically) because what is supporting the wall applies an equal and opposite force to mine for a net force of zero.
I would change the definition to say: Net forces are what cause changes in motion, which essentially is a statement of Newton's second law.
A more elementary definition of a force is a "push or pull", since that definition covers a force that doesn't necessarily result in a change in motion. See the discussion here:
What is the fundamental definition of force?
Hope this helps.
A: I don't follow this definition as motion is something associated mainly with velocity sometimes acceleration too. So if the object was moving with constant velocity then there won't be any net force acting on it. but if the motion had some acceleration there must be a net force acting on it.
It is important to note only net forces change motion but just forces don't do anything
So remember $\text{net force is mass times acceleration}$
A: In a strictly limited sense the definition is not necessarily wrong, just incomplete and potentially misleading. When a ball is at rest on a pool table and I strike it with my cue, I have used a force to impart motion on the ball. From a lay perspective this is entirely logical: force causes motion.
That's as far as it goes however, and this is where I - and most of the people answering this question - disapprove of this definition. It's a drastic over-simplification of what is happening, and not an enormously useful one. In fact it is this sort of simplified language that leads to serious misunderstandings of the way the world works. It's the scientific equivalent of baby talk, and there's no reason why it should be used at any level. Much better to use the most accurate language that can be understood at the level.
I'm not advocating that we teach tensor math and the field equations to children, just that we stop muddying their education with needless inaccuracies.
A: I think this definition is good enough, because all motion has been caused by some force (what else?). Except for the motion that is caused by your choice of frame of reference which is your abstraction that does not affect the real world phenomena.
Acceleration in physics is a characteristic of motion unlike the acceleration pedal being cause of motion when driving a car. One more argument, acceleration is even called the 'derivative' of motion(well, velocity to be precise..) for that reason.
