The owner of the tree is responsible for the damage caused by his good, in particular under the terms of articles 1465 and 1467 of the Civil code of Quebec (CcQ).
You are thus entitled by the law to ask your neighbour to compensate you for the damage caused. In the event of a refusal on his part, you can turn to the Court which will rule on the damage by evaluating the circumstances. The problem about which you complain must however be real and serious. Indeed, the neighbors must accept the normal disadvantages of having and being neighbours according to article 976 CcQ.
Beyond that, the Law envisages certain situations where the owner of the tree can be constrained to act. In particular, if the tree threatens to fall on the property of the neighbour, he will have to cut it or pull it straight again to avoid possible damage.
Also for example, if parts of the tree encroach on your grounds and if you wish that your neighbour cuts them, you will have to prove, if he refuses to follow up on your request, that there is a physical invasion by the branches or the roots of the tree and that this invasion harms your property seriously, under the terms of article 985 CcQ.
Beware, you may not carry out justice yourself.
It is important that you do not correct yourself the situation which worries you by cutting the branches or the roots of the tree of the neighbour which encroach on your property. Indeed, he could go to Court with you in his turn if you decide to do it. Moreover, the Court could condemn you to pay damage to your neighbour for having damaged or destroyed his good.
Privileging cordial neighbourly relations, the first stage in any conflict remains to make a clear statement of explanation on the situation to your neighbour.