Just seeking to clear up a bit of confusion. There seems to be a lot of points and counter points floating around so I will start at the beginning.
As I understand it a Artificer (RAW but perhaps not RAI) can cast V,S,M and V,S spells with both hands full. Let's assume one is a shield and one is a sword and at least one item is infused so as to act as his spell casting focus.
First, can they cast a V,S,M spell with no free hand?
Another example: a cleric’s holy symbol is emblazoned on her shield. She likes to wade into melee combat with a mace in one hand and a shield in the other. She uses the holy symbol as her spellcasting focus, so she needs to have the shield in hand when she casts a cleric spell that has a material component. If the spell, such as aid, also has a somatic component, she can perform that component with the shield hand and keep holding the mace in the other.
Second, can they cast V,S spells with no free hand?
This part seems easy. The answer is no. Nothing Material and hence no use of the arcane focus. However, if you read the Artificer Spellcasting section (emphasis added):
Tools Required You produce your artificer spell effects through your tools. You must have a spellcasting focus—specifically thieves’ tools or some kind of artisan’s tool—in hand when you cast any spell with this Spellcasting feature (meaning the spell has an ‘M’ component when you cast it). You must be proficient with the tool to use it in this way. See chapter 5, “Equipment,” in the Player’s Handbook for descriptions of these tools.
Since it clearly states any spell you cast has an 'M'. If the first is true and you can cast V,S,M with no free hand, then it goes to assume you can cast all spells as such.