旅 = to travel
留 = to stay
驻 = to station
The 旅 in 旅法学者 is short for 旅居 (sojourning)
旅法学者 = 旅居法国的外籍学者 is a scholar currently living in France as a foreigner.
The 留 in 留法學生 is short for 留学 (study abroad)
留法学生 = 留学法国的外籍留学生 is a foreign student studying in France
The 驻 in 驻法軍人 is short for 驻守 (station)
驻法軍人 = 驻守法国的外籍軍人 is a foreign soldier who stations in France
"旅X YY" describes an artist or scholar e.g. 旅法音樂家, 旅法作家, 旅法考古家, or simply a foreigner e.g. 旅美华人, 旅港加人
"留X 学生" describes students e.g. 留英学生, 留美学生, 留法学生
"驻X YY" describes an international organization, government, or military personnel e.g. CNN 驻英記者, 国际特赦组织驻俄監察員, 驻港大使, 驻中大使, 驻日美軍, 驻德美軍
访 in 访法学者 is short for 访问 (visiting) he can be visiting France for a few hours, a few days, or a few months; 旅法学者 usually staying in France for years or even for his or her entire life