It's often much deeper than the variation found in English, but yes, just about every language with a lot of speakers has a bunch of regional accents and dialects. They can often vary enough that it's very difficult for speakers on the other side of the country to understand, and enough so that it often makes sense to consider them separate languages. The dividing line isn't clear.

My wife speaks Cantonese with her family. Her parents can both speak Mandarin, and sometimes do that when they don't want the kids to understand, etc. Both parents also speak dialects from nearby regions that nobody else in the family can understand, and I'm told that they both have rather different accents when speaking Cantonese and Mandarin. And both of those dialects/languages have various regional accents too.

Much of my family speaks French. I don't speak it well at all now, but can understand Canadian French pretty much fluently, and can understand almost all of what I hear from most European French speakers too, but it's harder. There are some dialects in France where I have a terrible time though, and I've been to towns in Artois where I have no idea what they're saying. There's a huge range of accents in French.

Yup, strong regional differences are the norm.