The right of (legislative) initiative is the constitutionally defined power to propose a new law (bill).
The right of initiative is usually attributed to parliaments, which in most countries have the right to make law proposals, alone or sharing this right with the government.
In parliamentary systems it is common that both the government (executive) and the parliament have legislative initiative, but it also can be restricted to the government and the lower house of parliament, or even to the government alone.
In presidential systems legislative initiative usually only rests with the congress, such as in the United States. This, however, does not preclude the executive from suggesting the introduction of certain laws to their backers in the congress.
In France, ministerial bills are called law projects and parliament's bills are called law proposals.
In France, most of the bills are proposed by the government. One of the ministers propose the bill to those concerned by his application. Then, if the different ministers manage an agreement, the bill is sent to the and then to the Conseil d'État, the Council of Ministers, the Parliament, and so on... The Conseil d'État (and sometimes the Constitutional Council) has the duty to advise the government on law projects.
Any MP can propose a law to the parliament. Law proposals, unlike law projects, can be directly deposed if they do not increase the state's expenditure.
Both kind of bills can be first deposed to the Senate or the National Assembly